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Mechanism and Kinetics of Phase Separation in Polymer Solutions and Blends
Published in Yuri S. Lipatov, Anatoly E. Nesterov, Thermodynamics of Polymer Blends, 2020
Yuri S. Lipatov, Anatoly E. Nesterov
Another approach to the problem was proposed by Vrahopolou-Gilbert and McHugh.179 The mechanism of phase separation under flow is intimately connected with high molecular weight chain entanglements. Under flow, frictional forces cause the macromolecules to uncoil from their random quiescent conformation to a more extended state of lower conformational entropy. The effect of these processes on the chemical potential of the system can be considered in one of two ways. Either, a term for so-called “stored free energy” can be added to the Flory-Huggins expression for the free energy of mixing polymer and solvent, as done by Wolf. Or, one can visualize the effect of chain stretching as equivalent to introducing a degree of rigidity to the polymer coils whose thermodynamic properties then become those of a system of semiflexible chains.180 Frenkel suggested that stretching of macromolecular coil is equivalent to increasing its rigidity, thus shifting the binodal to higher concentrations and a higher critical temperature. To describe the situation, the effective flexibility parameter, f, proposed by Elyashevich181 is introduced, which depends on the extending force, F. The free energy change per mole of polymer associated with the application of flow (stored free energy) may be shown to be [] ΔGf=RT(x−2)ln[(1−f)(z−1)]
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Published in Chad A. Mirkin, Spherical Nucleic Acids, 2020
Mary X. Wang, Jeffrey D. Brodin, Jaime A. Millan, Soyoung E. Seo, Martin Girard, Monica Olvera de la Cruz, Byeongdu Lee, Chad A. Mirkin
By simulating both CsC1 and Th3P4 binary superlattices for a specific DNA design, the thermodynamically preferred structure between these two competing phases can be determined based on relative energetic differences and the entropies of their constituent DNA chains. Due to the complexity of DNA-NP lattices and the vast number of possible microstates, it is not feasible to calculate the DNA conformational entropy exactly. Instead, we calculated the volume accessible to the DNA chains (Vreee) as an estimation of conformational entropy. Energetic contributions (Utotal) were determined from a sum of hybridization energy (Uhybridization), the bond and angle energies due to distortions in the DNA chain (Uchain), and the excluded volume energy (Uexcluded) The enthalpy (H) can be estimated using H = Utotal+ PV, where P = 0 in our implicit solvent model [45]. The free energy difference between the CsCl and Th3P4 phases can be estimated using ΔF = Utoral — TΔS, where ΔS can be estimated as kBlogVfree. As observed experimentally, the CsCI structure is preferred for proteins with flexible ligands. As the number of spacers decreases and the DNA ligand rigidifies, the Th3P4 symmetry becomes more stable. Calculations show that this transition is due to a relative increase in Uchain and Vfree in flexible systems over rigid ones, indicating that, for systems with rigid sequences, the CsCl lattice is unfavorable due to arrangement of the DNA chains. Notably, flexible DNA strands explore 128% greater Vfree than rigid ones, supporting the idea that flexibility increases the conformational entropy of DNA ligands. This can be visualized in the diffuse distribution of sticky ends around the protein PAE when flexible DNA are used (Fig. 34.2C,D).
Calorimetry for studying the adsorption of proteins in hydrophobic interaction chromatography
Published in Preparative Biochemistry and Biotechnology, 2019
Agnes Rodler, Rene Ueberbacher, Beate Beyer, Alois Jungbauer
Most studies covered in this review focus on globular proteins containing ordered structural elements. In the native conformation globular proteins have reduced conformational entropy compared to the denatured state. The reason for this is the formation of structured elements (secondary structure) and domains stabilized by hydrogen bonds. The folding of a 10.000 Da protein containing approximately 50% secondary structure results in the loss of conformational entropy of several hundred J·K−1 resulting in a ΔG increase of several hundred kJ/mol.[118] In order for the globular structure to be stable this has to be compensated for by favorable interactions within the protein and/or between the protein and its environment. These interactions include hydrophobic, electrostatic and van der Waals interactions as well as hydrogen bonding. When folding into a globular structure, hydrophobic interactions lower the Gibbs energy around 500 kJ/mol because apolar amino acids are packed in the core of the protein.