van der Waals phase transition in protein solutions

The van der Waals equation of state for imperfect gases is applied to solutions of macromolecules, especially to explain the fluid-fluid phase transition in protein solutions, a phenomenon of much interest in relation to protein crystallization. The van der Waals b parameter corresponds to the total excluded volume per pair of molecules and can be calculated from independently known molecular properties. It is comprised of terms resulting from hard-sphere and net charge-charge interactions. The experimentally determined second virial coefficient B can then be used to obtain the equilibrium constant for dimerization K, a phenomenologically accessible measure of the van der Waals a parameter. Sedimentation equilibrium is recommended as the technique for measuring B most accurately. More general results are used to make a minor quantitative correction to the van der Waals prediction concerning the criterion for the fluid-fluid phase transition. Calculations of the effect of inert co-solutes on the phase transition may prove useful in choosing crystallization conditions

Critical behaviour and microscopic structure of charged AdS black holes via an alternative phase space

It has been argued that charged Ads black holes have similar thermodynamic behavior as the Van der Waals fluid system, provided one treats the cosmological constant as a thermodynamic variable in an extended phase space. In this paper, we disclose the deep connection between charged AdS black holes and Van der Waals fluid system without extending the phase space. We keep the cosmological constant as a fixed parameter and instead, treat the square of the charge of black hole as a thermodynamic variable. Therefore, we write the equation of state as $Q^{2}=Q^{2}(T,\Psi)$ where $\Psi$ (conjugate of $Q^{2}$) is the inverse of the specific volume, $\Psi=1/v$. This allows us to complete the analogy of charged AdS black holes with Van der Waals fluid system and derive the phase transition as well as critical exponents of the system. We identify a thermodynamic instability in this new picture with real analogy to Van der Waals fluid with physically relevant Maxwell construction. We therefore study the critical behavior of isotherms in $$ diagram and deduce all the critical exponents of the system and determine that the system exhibits a small-large black hole phase transition at the critical point $(T_c,Q^2_c, \Psi_c)$. This alternative view is important as one can imagine such a change for a given single black hole i. e. acquiring charge which induces the phase transition. Finally, we disclose the microscopic properties of charged AdS black holes by using thermodynamic geometry. Interestingly, we find that scalar curvature has a gap between small and large black holes, and this gap becomes exceedingly large as one moves away from the critical point along the transition line. Therefore, we are able to attribute the sudden enlargement of the black hole to the strong repulsive nature of the internal constituents at the phase transition.Comment: 7 pages, 6 figures. New title and a new figure in the second versio

Thermodynamic extended phase space and P−VP-V criticality of black holes at Pure Lovelock gravity

In this work the \textit{chemistry} of asymptotically AdS black hole, charged and uncharged, solutions of Pure Lovelock gravity is discussed. For this the mass parameter of black holes is identified with the enthalpy of the system together with the promotion of the cosmological constant to a thermodynamics variable proportional to the \textit{pressure} of the system. The equations of state for both, charged and uncharged, are obtained. It is shown that the charged case behaves as a Van der Waals fluid. The existence of a first order phase transition between small stable/large stable black hole, which is a reminiscent of the liquid/gas transition, is found. The critical exponents of the thermal evolution, for different cases of interest, are similar to those of the Van der Waals fluid