Two-chamber lattice model for thermodiffusion in polymer solutions

When a temperature gradient is applied to a polymer solution, the polymer typically migrates to the colder regions of the fluid as a result of thermal diffusion (Soret effect). However, in recent thermodiffusion experiments on poly(ethylene-oxide) (PEO) in a mixed ethanol/water solvent it is observed that for some solvent compositions the polymer migrates to the cold side, while for other compositions it migrates to the warm side. In order to understand this behavior, we have developed a two-chamber lattice model approach to investigate thermodiffusion in dilute polymer solutions. For a short polymer chain in an incompressible, one-component solvent we obtain exact results for the partitioning of the polymer between a warm and a cold chamber. In order to describe mixtures of PEO, ethanol, and water, we have extended this simple model to account for compressibility and hydrogen bonding between PEO and water molecules. For this complex system, we obtain approximate results for the composition in the warmer and cooler chambers that allow us to calculate Soret coefficients for given temperature, pressure, and solvent composition. The sign of the Soret coefficient is found to change from negative (polymer enriched in warmer region) to positive (polymer enriched in cooler region) as the water content of the solution is increased, in agreement with experimental data. We also investigate the temperature dependence of the Soret effect and find that a change in temperature can induce a change in the sign of the Soret coefficient. We note a close relationship between the solvent quality and the partitioning of the polymer between the two chambers, which may explain why negative Soret coefficients for polymers are so rarely observed.Comment: 12 pages, 8 figure

Local and chain dynamics in miscible polymer blends: A Monte Carlo simulation study

Local chain structure and local environment play an important role in the dynamics of polymer chains in miscible blends. In general, the friction coefficients that describe the segmental dynamics of the two components in a blend differ from each other and from those of the pure melts. In this work, we investigate polymer blend dynamics with Monte Carlo simulations of a generalized bond-fluctuation model, where differences in the interaction energies between non-bonded nearest neighbors distinguish the two components of a blend. Simulations employing only local moves and respecting a non-bond crossing condition were carried out for blends with a range of compositions, densities, and chain lengths. The blends investigated here have long-chain dynamics in the crossover region between Rouse and entangled behavior. In order to investigate the scaling of the self-diffusion coefficients, characteristic chain lengths $N_\mathrm{c}$ are calculated from the packing length of the chains. These are combined with a local mobility $\mu$ determined from the acceptance rate and the effective bond length to yield characteristic self-diffusion coefficients $D_\mathrm{c}=\mu/N_\mathrm{c}$. We find that the data for both melts and blends collapse onto a common line in a graph of reduced diffusion coefficients $D/D_\mathrm{c}$ as a function of reduced chain length $N/N_\mathrm{c}$. The composition dependence of dynamic properties is investigated in detail for melts and blends with chains of length twenty at three different densities. For these blends, we calculate friction coefficients from the local mobilities and consider their composition and pressure dependence. The friction coefficients determined in this way show many of the characteristics observed in experiments on miscible blends.Comment: 12 pages, 13 figures, editorial change

Transitions of tethered polymer chains: A simulation study with the bond fluctuation lattice model

A polymer chain tethered to a surface may be compact or extended, adsorbed or desorbed, depending on interactions with the surface and the surrounding solvent. This leads to a rich phase diagram with a variety of transitions. To investigate these transitions we have performed Monte Carlo simulations of a bond-fluctuation model with Wang-Landau and umbrella sampling algorithms in a two-dimensional state space. The simulations' density of states results have been evaluated for interaction parameters spanning the range from good to poor solvent conditions and from repulsive to strongly attractive surfaces. In this work, we describe the simulation method and present results for the overall phase behavior and for some of the transitions. For adsorption in good solvent, we compare with Metropolis Monte Carlo data for the same model and find good agreement between the results. For the collapse transition, which occurs when the solvent quality changes from good to poor, we consider two situations corresponding to three-dimensional (hard surface) and two-dimensional (very attractive surface) chain conformations, respectively. For the hard surface, we compare tethered chains with free chains and find very similar behavior for both types of chains. For the very attractive surface, we find the two-dimensional chain collapse to be a two-step transition with the same sequence of transitions that is observed for three-dimensional chains: a coil-globule transition that changes the overall chain size is followed by a local rearrangement of chain segments.Comment: 17 pages, 12 figures, to appear in J. Chem. Phy

Configurational contribution to the Soret effect of a protein ligand system

Many of the biological functions of proteins are closely associated with their ability to bind ligands and change conformations in response to changing conditions. Since binding state and conformation of a protein affect its response to a temperature gradient, they may be probed with thermophoresis. In recent years, thermophoretic techniques to investigate biomolecular interactions, quantify ligand binding, and probe conformational changes have become established. To develop a better understanding of the mechanisms underlying the thermophoretic behavior of proteins and ligands, we employ a simple, off-lattice model for a protein and ligand in explicit solvent. To investigate the partitioning of the particles in a temperature gradient, we perform Wang-Landau-type simulations in a divided simulation box and construct the density of states over a two-dimensional state space. This method gives us access to the entropy and energy of the divided system and allows us to estimate the configurational contribution to the Soret coefficient. In this work, we focus on dilute solutions of hydrophobic proteins and investigate the effect of ligand binding on their thermophoretic behavior. We find that our simple model captures important aspects of protein-ligand interactions and allows us to relate the binding energy to the change in Soret coefficient upon ligand binding

Transitions of Tethered Chain Molecules under Tension

An applied tension force changes the equilibrium conformations of a polymer chain tethered to a planar substrate and thus affects the adsorption transition as well as the coil-globule and crystallization transitions. Conversely, solvent quality and surface attraction are reflected in equilibrium force-extension curves that can be measured in experiments. To investigate these effects theoretically, we study tethered chains under tension with Wang-Landau simulations of a bond-fluctuation lattice model. Applying our model to pulling experiments on biological molecules we obtain a good description of experimental data in the intermediate force range, where universal features dominate and finite size effects are small. For tethered chains in poor solvent, we observe the predicted two-phase coexistence at transitions from the globule to stretched conformations and also discover direct transitions from crystalline to stretched conformations. A phase portrait for finite chains constructed by evaluating the density of states for a broad range of solvent conditions and tensions shows how increasing tension leads to a disappearance of the globular phase. For chains in good solvents tethered to hard and attractive surfaces we find the predicted scaling with the chain length in the low-force regime and show that our results are well described by an analytical, independent-bond approximation for the bond-fluctuation model for the highest tensions. Finally, for a hard or slightly attractive surface the stretching of a tethered chain is a conformational change that does not correspond to a phase transition. However, when the surface attraction is sufficient to adsorb a chain it will undergo a desorption transition at a critical value of the applied force. Our results for force-induced desorption show the transition to be discontinuous with partially desorbed conformations in the coexistence region

Partition Function Zeros and Finite Size Scaling for Polymer Adsorption

The zeros of the canonical partition functions for a flexible polymer chain tethered to an attractive flat surface are computed for chains up to length N = 1536. We use a bond-fluctuation model for the polymer and obtain the density of states for the tethered chain by Wang-Landau sampling. The partition function zeros in the complex e(β)-plane are symmetric about the real axis and densest in a boundary region that has the shape of a nearly closed circle, centered at the origin, terminated by two flaring tails. This structure defines a root-free zone about the positive real axis and follows Yang-Lee theory. As the chain length increases, the base of each tail moves toward the real axis, converging on the phase-transition point in the thermodynamic limit. We apply finite-size scaling theory of partition-function zeros and show that the crossover exponent defined through the leading zero is identical to the standard polymer adsorption crossover exponent ϕ. Scaling analysis of the leading zeros locates the polymer adsorption transition in the thermodynamic (N → ∞) limit at reduced temperature Tc (*)=1.027(3) [βc=1/Tc (*)=0.974(3)] with crossover exponent ϕ = 0.515(25). Critical exponents for the order parameter and specific heat are determined to be β̃=0.97(5) and α = 0.03(4), respectively. A universal scaling function for the average number of surface contacts is also constructed

Thermodiffusion of aqueous solutions of various potassium salts

Thermophoresis or thermodiffusion has become an important tool to monitor protein-ligand binding as it is very sensitive to the nature of solute-water interactions. However, the microscopic mechanisms underlying thermodiffusion in protein systems are poorly understood at this time. One reason is the difficulty to separate the effects of the protein system of interest from the effects of buffers that are added to stabilize the proteins. Due to the buffers, typical protein solutions form multicomponent mixtures with several kinds of salt. To achieve a more fundamental understanding of thermodiffusion of proteins, it is therefore necessary to investigate solutions of buffer salts. For this work, the thermodiffusion of aqueous potassium salt solutions has been studied systematically. We use thermal diffusion forced Rayleigh scattering experiments in a temperature range from 15 degrees C to 45 degrees C to investigate the thermodiffusive properties of aqueous solutions of five potassium salts: potassium chloride, potassium bromide, potassium thiocyanate, potassium acetate, and potassium carbonate in a molality range between 1 mol/kg and 5 mol/kg. We compare the thermophoretic results with those obtained for non-ionic solutes and discuss the thermophoresis of the salts in the context of ion-specific solvation according to the Hofmeister series

Sign change of the Soret coefficient of poly(ethylene oxide) in water/ethanol mixtures observed by thermal diffusion forced Rayleigh scattering

Soret coefficients of the ternary system of poly(ethylene oxide) in mixed water/ethanol solvent were measured over a wide solvent composition range by means of thermal diffusion forced Rayleigh scattering. The Soret coefficient S(T) of the polymer was found to change sign as the water content of the solvent increases with the sign change taking place at a water mass fraction of 0.83 at a temperature of 22 degrees C. For high water concentrations, the value of S(T) of poly(ethylene oxide) is positive, i.e., the polymer migrates to the cooler regions of the fluid, as is typical for polymers in good solvents. For low water content, on the other hand, the Soret coefficient of the polymer is negative, i.e., the polymer migrates to the warmer regions of the fluid. Measurements for two different polymer concentrations showed a larger magnitude of the Soret coefficient for the smaller polymer concentration. The temperature dependence of the Soret coefficient was investigated for water-rich polymer solutions and revealed a sign change from negative to positive as the temperature is increased. Thermodiffusion experiments were also performed on the binary mixture water/ethanol. For the binary mixtures, the Soret coefficient of water was observed to change sign at a water mass fraction of 0.71. This is in agreement with experimental results from the literature. Our results show that specific interactions (hydrogen bonds) between solvent molecules and between polymer and solvent molecules play an important role in thermodiffusion for this system