Role of the interaction range in the shaping of phase diagrams in simple fluids. The hard sphere Yukawa fluid as a case study

On the dynamically arrested states of equilibrium and non-equilibrium gels: a comprehensive Brownian dynamics study

In this work a systematic study over a wide number of final thermodynamic states for two gel-forming liquids was performed. Such two kind of gel formers are distinguished by their specific interparticle interaction potential. We explored several thermodynamic states determining the thermodynamic, structural and dynamic properties of both liquids after a sudden temperature change. The thermodynamic analysis allows to identify that the liquid with short range attraction and long range repulsion lacks of a stable gas-liquid phase separation liquid, in contrast with the liquid with short range attractions. Thus, although for some thermodynamic states the structural behavior, measured by the static structure factor, is similar to and characteristic of the gel phase, for the short range attractive fluid the gel phase is a consequence of a spinodal decomposition process. In contrast, gelation in the short range attraction and long range repulsion liquid is not due to a phase separation. We also analyze the similarities and differences of the dynamic behavior of both systems through the analysis of the mean square displacement, the self part of the intermediate scattering function, the diffusion coefficient and theαrelaxation time. Finally, using one of the main results of the non-equilibrium self-consistent generalized Langevin equation theory (NE-SCGLE), we determine the dynamic arrest phase diagram in the volume fraction and temperature (φvsT) plane.

The generalized continuous multiple step (GCMS) potential: model systems and benchmarks

The generalized continuous multiple step (GCMS) potential is presented in this work. Its flexible form allows forrepulsiveand/orattractivecontributions to be encoded through adjustable energy and length scales. The GCMS interaction provides a continuous representation of square-well, square-shoulder potentials and their variants for implementation in computer simulations. A continuous and differentiable energy representation is required to derive forces in conventional simulation algorithms. Molecular dynamics simulations are of particular interest when considering the dynamic properties of a system. The GCMS potential can mimic other interactions with a judicious choice of parameters due to the versatile sigmoid form. In this study, our benchmarks for the GCMS representation include triangular, Yukawa, Franzese, and Lennard-Jones potentials. Comparisons made with published data on volumetric phase diagrams, liquid structure, and diffusivity from model systems are in excellent agreement.

Molecular fields and statistical field theory of fluids: Application to interface phenomena

Using the integral transformation, the field-theoretical Hamiltonian of the statistical field theory of fluids is obtained along with the microscopic expressions for the coefficients of the Hamiltonian. Applying this approach to the liquid-vapor interface, we derive an explicit analytical expression for the surface tension in terms of temperature, density, and parameters of the intermolecular potential. We also demonstrate that a clear physical interpretation may be given to the formal statistical field arising in the integral transformation-it may be associated with the one-body local microscopic potential. The results of the theory, lacking any ad hoc or fitting parameters are in good agreement with available simulation data.

Phase-Separation Kinetics in Protein-Salt Mixtures with Compositionally Tuned Interactions

Liquid-liquid phase separation (LLPS) in protein systems is relevant for many phenomena, from protein condensation diseases to subcellular organization to possible pathways toward protein crystallization. Understanding and controlling LLPS in proteins is therefore highly relevant for various areas of (biological) soft matter research. Solutions of the protein bovine serum albumin (BSA) have been shown to have a lower critical solution temperature-LLPS (LCST-LLPS) induceable by multivalent salts. Importantly, the nature of the multivalent cation used influences the LCST-LLPS in such systems. Here, we present a systematic ultrasmall-angle X-ray scattering investigation of the kinetics of LCST-LLPS of BSA in the presence of different mixtures of HoCl₃ and LaCl₃, resulting in different effective interprotein attraction strengths. We monitor the characteristic length scales ξ( t, T_fin) after inducing LLPS by subjecting the respective systems to temperature jumps in their liquid-liquid coexistence regions. With increasing interprotein attraction and increasing T_fin, we observe an increasing deviation from the growth law of ξ ∼ t^1/3 and an increased trend toward arrest. We thus establish a multidimensional method to tune phase transitions in our systems. Our findings help shed light on general questions regarding LLPS and the tunability of its kinetics in both proteins and colloidal systems.

Tuning phase transitions of aqueous protein solutions by multivalent cations

In the presence of trivalent cations, negatively charged globular proteins show a rich phase behaviour including reentrant condensation, crystallisation, clustering and lower critical solution temperature metastable liquid-liquid phase separation (LCST-LLPS). Here, we present a systematic study on how different multivalent cations can be employed to tune the interactions and the associated phase behaviour of proteins. We focus our investigations on the protein bovine serum albumin (BSA) in the presence of HoCl3, LaCl3 and YCl3. Using UV-Vis spectroscopy and small-angle X-ray scattering (SAXS), we find that the interprotein attraction induced by Ho3+ is very strong, while the one induced by La3+ is comparatively weak when comparing the data to BSA-Y3+ systems based on our previous work. Using zeta potential and isothermal titration calorimetry (ITC) measurements, we establish different binding affinities of cations to BSA with Ho3+ having the highest one. We propose that a combination of different cation features such as radius, polarisability and in particular hydration effects determine the protein-protein interaction induced by these cations. Our findings imply that subtle differences in cation properties can be a sensitive tool to fine-tune protein-protein interactions and phase behaviour in solution.

Kirkwood-Buff integrals for hard-core Yukawa fluids

The Kirkwood-Buff (KB) theory of solution is employed to investigate several macroscopic properties of the one-component hard-core Yukawa (HCY) fluid, where the key physical quantities are the KB integrals (KBIs). For both repulsive and attractive HCY fluids, the radial distribution functions are calculated by using the classical density functional theory, and then the corresponding KBIs are carried out. Since the local structure and global properties of a fluid can be related by KBI, we presented the isothermal compressibility and the derivative of the chemical potential with respect to bulk density for both repulsive and attractive HCY fluids. It is found that a transition of the affinity of particles in an attractive HCY fluid exists. The corresponding phase diagrams on the affinity are illustrated, which consist of repulsive and attractive regions with the boundary line of KBIs being zero. These results show that the aggregated structure of a HCY fluid can be effectively regulated by the screening parameter, bulk density and interaction energy, while KBIs can provide a quantitative reliable description on the properties of HCY fluids.

Tuning the bridging attraction between large hard particles by the softness of small microgels

In this study, the attraction between large hard polystyrene (PS) spheres is studied by using three types of small microgels as bridging agents. One is a purely soft poly(N-isopropylacrylamide) (PNIPAM) microgel, the other two have a non-deformable PS hard core surrounded by a soft PNIPAM shell but are different in the core-shell ratio. The affinity for bridging the large PS spheres is provided and thus affected by the PNIPAM constituent in the microgels. The bridging effects caused by the microgels can be indirectly incorporated into their influence on the effective attraction interaction between the large hard spheres, since the size of the microgels is very small in comparison to the size of the PS hard spheres. At a given volume fraction of large PS spheres, they behave essentially as hard spheres in the absence of small microgels. By gradually adding the microgels, the large spheres are connected to each other through the bridging of small particles until the attraction strength reaches a maximum value, after which adding more small particles slowly decreases the effective attraction strength and eventually the large particles disperse individually when saturated adsorption is achieved. The aggregation and gelation behaviors triggered by these three types of small microgels are compared and discussed. A way to tune the strength and range of the short-range attractive potential via changing the softness of bridging microgels (which can be achieved either by using core-shell microgels or by changing the temperature) is proposed.

Critical asymmetry in renormalization group theory for fluids

The renormalization-group (RG) approaches for fluids are employed to investigate critical asymmetry of vapour-liquid equilibrium (VLE) of fluids. Three different approaches based on RG theory for fluids are reviewed and compared. RG approaches are applied to various fluid systems: hard-core square-well fluids of variable ranges, hard-core Yukawa fluids, and square-well dimer fluids and modelling VLE of n-alkane molecules. Phase diagrams of simple model fluids and alkanes described by RG approaches are analyzed to assess the capability of describing the VLE critical asymmetry which is suggested in complete scaling theory. Results of thermodynamic properties obtained by RG theory for fluids agree with the simulation and experimental data. Coexistence diameters, which are smaller than the critical densities, are found in the RG descriptions of critical asymmetries of several fluids. Our calculation and analysis show that the approach coupling local free energy with White's RG iteration which aims to incorporate density fluctuations into free energy is not adequate for VLE critical asymmetry due to the inadequate order parameter and the local free energy functional used in the partition function.

Liquid-vapor phase diagram and surface properties in oppositely charged colloids represented by a mixture of attractive and repulsive Yukawa potentials

The liquid-vapor phase diagrams of equal size diameter σ binary mixtures of screened potentials have been reported for several ranges of interaction using Monte Carlo simulation methods [J. B. Caballero, A. M. Puertas, A. Ferńandez-Barbero, F. J. de las Nieves, J. M. Romero-Enrique, and L. F. Rull, J. Chem. Phys. 124, 054909 (2006); A. Fortini, A.-P. Hynninen, and M. Dijkstra, J. Chem. Phys. 125, 094502 (2006)]. Both works report controversial results about the stability of the phase diagram with the inverse Debye screening length κ. Caballero found stability for values of κσ up to 20 while Fortini reported stability for κσ up to 20 while Fortini reported stability for κσ ≤ 4. In this work a spinodal decomposition process where the liquid and vapor phases coexist through an interface in a slab geometry is used to obtain the phase equilibrium and surface properties using a discontinuous molecular dynamics simulations for mixtures of equal size particles carrying opposite charge and interacting with a mixture of attractive and repulsive Yukawa potentials at different values of κσ. An crude estimation of the triple point temperatures is also reported. The isothermal-isobaric method was also used to determine the phase stability using one phase simulations. We found that liquid-vapor coexistence is stable for values of κσ > 20 and that the critical temperatures have a maximum value at around κσ = 10, in agreement with Caballero et al. calculations. There also exists a controversy about the liquid-vapor envelope stability of the pure component attractive Yukawa model which is also discussed in the text. In addition, details about the equivalence between continuous and discontinuous molecular dynamics simulations are given, in the Appendix, for Yukawa and Lennard-Jones potentials.

Optimum free energy in the reference functional approach for the integral equations theory

We investigate the question of determining the bulk properties of liquids, required as input for practical applications of the density functional theory of inhomogeneous systems, using density functional theory itself. By considering the reference functional approach in the test particle limit, we derive an expression of the bulk free energy that is consistent with the closure of the Ornstein-Zernike equations in which the bridge functions are obtained from the reference system bridge functional. By examining the connection between the free energy functional and the formally exact bulk free energy, we obtain an improved expression of the corresponding non-local term in the standard reference hypernetted chain theory derived by Lado. In this way, we also clarify the meaning of the recently proposed criterion for determining the optimum hard-sphere diameter in the reference system. This leads to a theory in which the sole input is the reference system bridge functional both for the homogeneous system and the inhomogeneous one. The accuracy of this method is illustrated with the standard case of the Lennard-Jones fluid and with a Yukawa fluid with very short range attraction.

A study of the pair and triplet structures of the quantum hard-sphere Yukawa fluid

The pair and triplet structures of the quantum hard-sphere Yukawa fluid, evaluated for equilateral and isosceles correlations in both the r and the k spaces for a range of conditions and with a particular focus on a region where the onset of increasing number fluctuations takes place (for densities 0.4<or=rho(N) ( *)<or=0.5, along the isotherm lambda(B) ( *)=0.6), are computed via path-integral Monte Carlo simulations in the canonical ensemble and an appropriate Ornstein-Zernike framework. For a given type of correlation (instantaneous, continuous linear response, and centroids), the structural results in r space display how the correlation functions approach each other with decreasing densities as a result of the increasing fluctuations. An attempt at obtaining improved isothermal compressibilities by using a simplified grand-canonical correction to the canonical pair radial functions is also discussed in detail. The results for triplets in k space are based on triplet direct correlation function calculations and are restricted to the higher-density region of the interval studied. Complementary results report an assessment of the performances of the Kirkwood superposition and the Jackson-Feenberg convolution. Comparisons with results also obtained in this work for the bare quantum and the classical hard-sphere fluids are made, allowing one to draw conclusions on the interplay between the inclusion of Yukawa attractions and the quantum diffraction effects in hard-sphere fluids.

Reformulation of liquid perturbation theory for low temperatures

A perturbation strategy is proposed which allows liquid perturbation methodology to be applied to extremely low temperature situations for which the available liquid integral equation theory and traditional thermodynamic perturbation theory fail. The possibility of avoiding the low temperature problem of the thermodynamic perturbation theory not only is of relevance to the investigation of complex fluids, but also may be useful for reformulation of other liquid theories to achieve higher accuracy and avoid the respective low temperature problems.

Residual multiparticle entropy does not generally change sign near freezing

The residual multiparticle entropy (RMPE) of two- and three-dimensional fluids changes sign near the freezing line, providing a quasiuniversal "one-phase" rule for the location of the liquid-solid transition. We present new simulation results for d-dimensional hard-sphere fluids (d=1-5) which show, however, that this freezing criterion fails in other spatial dimensions. The results also call into question the idea that a change in sign of the RMPE implies the emergence of a new kind of local structural order in the fluid.

Novel perturbation approach for the structure factor of the attractive hard-core Yukawa fluid

A novel perturbation approach for the structure factor S(k) of the Lennard-Jones-type Yukawa fluid with z=1.8 is presented. An approach is based on a new reference system, that is, the short-range Yukawa model with z0>z=1.8. By choosing for the reference system the value z0=6, it is shown that (i) the proposed approach for S(k) performs much better than the traditional hard-sphere reference perturbation method does; (ii) the use of an approximate mean spherical (MSA) description of the reference structure factor provides the results for S(k) that are more accurate as those obtained from the direct MSA computations; and (iii) the results obtained for S(k) tend to reproduce "exact" simulation results when accurate simulation data for the reference system are used.

Phase diagram and surface tension of the hard-core attractive Yukawa model of variable range: Monte Carlo simulations

The liquid-vapor phase diagram and surface tension for hard-core Yukawa potential with 4<or=kappa<or=7 are calculated by applying canonical Monte Carlo simulation. The authors' new simulation results are more precise than those reported before, which allows them to affirm the accuracy of the previously reported self-consistent Ornstein-Zernike approximation calculations for kappa=5 and 7.

Phase diagrams of alkali halides using two interaction models: A molecular dynamics and free energy study

Phase diagrams for potassium and sodium chlorides are determined by molecular dynamics and free energy calculations. Two rigid-ion interaction models, namely, the Born-Mayer-Huggins (BMH) and Michielsen-Woerlee-Graaf (MWG) effective pair potentials, have been used. The critical and triple point properties are discussed and compared with available experimental and simulation data. The MWG model reproduces the experimental liquid-gas equilibria better than the BMH model, being the accordance very good in the lowest temperature region of the coexistent liquids, particularly for NaCl. However, both models underestimate the critical temperatures of KCl and NaCl. Relatively to the solid-gas equilibria, the models do not reproduce well the experimental data. As for the solid-liquid coexistences either the BMH or the MWG models appear unrealistic.

Secondary Minimum Coagulation in Charged Colloidal Suspensions from Statistical Mechanics Methods

A statistical mechanics approach is applied to predict the critical parameters of coagulation in the secondary minimum for charged colloidal suspensions. This method is based on the solution of the reference hypernetted chain (RHNC) integral equation, and it is intended to estimate only the locus of the critical point instead of the full computation of the "gas-liquid" coexistence. We have used an extrapolation procedure due to the lack of solution of the integral equation in the vicinity of the critical point. Knowing that the osmotic isothermal compressibility of the colloidal system should ideally diverge in the critical point, we work out the critical salt concentration for which the inverse of the compressibility should be zero. This extrapolation procedure is more rapid than that previously proposed by Morales and co-workers [Morales, V.; Anta, J. A.; Lago, S. Langmuir 2003, 19, 475], and it is shown to give equivalent results. We also present experimental results about secondary minimum coagulation for polystyrene latexes and use our method to reproduce the experimental trends. The comparison between theory and experiment is quite good for all colloidal diameters studied.

Phase diagram of the hard-core Yukawa fluid within the integral equation method

In this study, the integral equation method proposed recently by Sarkisov [J. Chem. Phys. 114, 9496 (2001).], which has proved accurate for continuous potentials, is extended successfully to the hard sphere potential plus an attractive Yukawa tail. By comparing the results of thermodynamic properties, including the liquid-vapor phase diagram, with available simulation data, it is found that this method remains reliable for this class of models of interaction often used in colloid science.

Improvement on macroscopic compressibility approximation and beyond

A numerical procedure is proposed to extend the thermodynamic perturbation expansion (TPE) to a higher order. It is shown that the present second order term is superior to that due to a macroscopic compressibility approximation (MCA), a local compressibility approximation, and a superposition approximation by Barker and Henderson [Rev. Mod. Phys. 48, 587 (1976)]. Extensive model calculation and comparison with simulation data available in literature and supplied in the present report indicate that the present third order TPE is superior to a previous second order TPE based on the MCA, two previous perturbation theories, which are respectively based on an analytical mean spherical approximation for an Ornstein-Zernike equation, and an assumed explicit functional form for the Laplace transform of radial distribution function multiplied by radial distance, and a recent generalized van der Waals theory. The present critical temperature for a hard core attractive Yukawa fluid of varying range is in very good agreement with that due to a hierarchical reference theory. The present third order TPE is computationally far more modest than the self-consistent integral equation theory, and therefore is a viable alternative to use of the latter.

Phase coexistence in polydisperse multi-Yukawa hard-sphere fluid: high temperature approximation

High temperature approximation (HTA) is used to describe the phase behavior of polydisperse multi-Yukawa hard-sphere fluid mixtures. It is demonstrated that in the frames of the HTA the model belongs to the class of "truncatable free energy models," i.e., the models with thermodynamical properties (Helmholtz free energy, chemical potential, and pressure) defined by the finite number of generalized moments. Using this property we were able to calculate the complete phase diagram (i.e., cloud and shadow curves as well as binodals) and size distribution functions of the coexisting phases of several different models of polydisperse fluids. In particular, we consider polydisperse one-Yukawa hard-sphere mixture with factorizable Yukawa coefficients and polydisperse Lennard-Jones (LJ) mixture with interaction energy parameter and/or size polydispersity. To validate the accuracy of the HTA we compare theoretical results with previously published results of more advanced mean spherical approximation (MSA) for the one-Yukawa model and with the Monte Carlo (MC) computer simulation results of [Wilding et al. J. Chem. Phys. 121, 6887 (2004); Phys. Rev. Lett. 95, 155701 (2005)] for the LJ model. We find that overall predictions of the HTA are in reasonable agreement with predictions of the MSA and MC, with the accuracy range from semiquantitative (for the phase diagram) to quantitative (for the size distribution functions).