Excluded Volume Forces Research Articles

Structure and thermodynamics of droplets with end-grafted polymer-chains of Pickering emulsions from Molecular Dynamics Simulations and Scaling-Theory

We consider a Pickering emulsion (oil-in-water or water-in-oil types) formed by a low-density assembly of droplets (dispersed phase) with end-grafted polymer-chains, which are dispersed in another liquid (continuous phase). The role of the added polymer is to stabilize the emulsion due the excluded volume forces between monomers. Initially, the polymer-chains are anchored onto the droplets surfaces via big amphiphile molecules and then float in the continuous phase (good solvent). As demonstrated very recently, the hairy-droplets interact mutually through an effective pair-potential which is the sum of a steric repulsive part coming from the repulsion between monomers and a van der Waals attractive one. Such a potential depends on the interdistance between adjacent hairy-droplets, their size, the bath temperature, the Hamaker’s constant, the number of grafted-polymer-chains per droplet (or equivalently the grafting-density) and their molecular-weight. The goal of this work is an extensive study of the structural and thermodynamical properties of the dispersion, using Molecular Dynamics Simulations (MDS). We note that for our study, the varied pertinent parameter is the grafting-density keeping fixed the other parameters of the problem. First , we investigate the structure of the dispersed hairy-droplets through the computation of the radial distribution function (RDF), using MDS. Second , we introduce a Scaling-Theory to investigate the hairy-droplets aggregation. The latter approach allows the determination of the fractal dimension of the hairy-droplets aggregates. Third , from the computed RDF, we extract all the thermodynamical quantities which are the virial-pressure, the internal-energy and the isothermal-compressibility. We note that our results from MSD agree well with the theoretical predictions we have deduced from Statistical Mechanics Principles. Finally, a possible link of our simulations to experiment is also discussed. • Systematic study of structure of Pickering emulsions from Molecular Dynamics Simulations. • Investigation of thermal properties of Pickering emulsions from Molecular Dynamics Simulations. • Elaboration of a scaling-theory for aggregation study. • Rigorous results from Statistical Mechanics. • Role of the grafting-density of anchored polymer-chains onto interface between dispersed and continuous phases.

Structure formation in suspensions under uniform electric or magnetic field

The structure formation of particles with induced dipoles dispersed in a viscous fluid, under a spatially and temporarily uniform external electric or magnetic field, is investigated by means of Brownian Dynamics simulations. Dipole–dipole interactions forces, excluded volume forces and thermal fluctuations are accounted for. The resulting structures are characterized in terms of average orientation of their inter-particle vectors (second Legendre polynomial), network structure, size of particle clusters, anisotropy of the gyration tensor of every cluster and existence of (cluster) percolation. The magnitude of the strength of the external field and the volume fraction of particles are varied and the structural evolution of the system is followed in time. The results show that the characteristic timescale calculated from the interaction of only two dipoles is also valid for the collective dynamics of many-particle simulations. In addition, the magnitude of the strength of the external field in the range of values we investigate influences only the magnitude of the deviations around the average behavior. The main characteristics (number density of branch-points and thickness of branches) of the structure are mainly affected by the volume fraction. The possibility of 3D printing these systems is explored. While the paper provides the details about the case of an electric field, all results presented here can be translated directly into the case of a magnetic field and paramagnetic particles.

Effective pair-potentials between droplets with end-grafted polymers within Pickering emulsions versus grafting-density, solvent quality and monomer concentration and phase diagrams architectures

The aim is a quantitative determination of the effective pair-potentials between droplets within Pickering emulsions of (oil-in-water or water-in-oil types), which are protected by end-grafted polymer-chains via (uncharged) big solid particles. This strong and irreversible grafting mode plays a fundamental role and rends the emulsions more stable, even in the absence of the charges. The droplets stabilization is very sensitive to the bath temperature that controls the solvent quality, the number of grafted-polymers per droplet (or grafting-density), and the concentration of monomers that float in the continuous phase (water or oil). The effective interaction between the hairy-droplets is a sum of two parts: the steric interaction coming from the excluded-volume forces, and the second is simply the usual van der Waals attraction. First, taking advantage of those results already derived using Renormalization Theory techniques, we determine the expression of the repulsive part of the overall pair-potentials, for all distances between the interacting hairy-droplets. Second, we study all the analytic properties of the obtained overall pair-potential, taking into account the solvent quality, the values of the bulk monomer concentration and the grafting-density. Third, these analytic properties enable us to classify the various shapes of the pair-potentials in space of the pertinent parameters. In particular, in any case (good and theta-solvents), we observe that, for high-grafting-densities (above some known critical value) or small monomer concentration (below some known critical value), the potentials exhibit an energy barrier that prevents the coalescence of the hairy-droplets. As remark, incidentally, the determined expressions of the pair-potentials are very similar to those of the DLVO potentials. Fourth, we draw the architectures of the phase diagrams in the (N,f)-plan, for dilute solutions, and in (f,Φ0)-plan, for semi-dilute solutions, where N, f and Φ0 denote the polymerization degree of the grafted-polymer-chains, their number per hairy-droplet and the monomer volume fraction, respectively. Finally, we discuss a link of the present work to experiment.

Folding of an Unfolded Protein by Macromolecular Crowding in Vitro

Protein folding in vivo takes place in a highly crowded environment. The resulting excluded volume forces are thought to stabilize folded forms of proteins. In agreement, many in vitro studies have shown that the presence of macromolecular crowding agents increases the stability of folded proteins but often by only a few kJ per mol. Although it should not matter at what position in the transition between folded and unfolded forms the effect of crowding is employed, there have been no studies assessing whether excluded volume forces alone can correctly fold polypeptides that are mostly unfolded. However, some studies have indicated that the effect of crowding becomes larger the more destabilized the protein is (but still being folded), suggesting that the crowding effect may be exaggerated for unfolded proteins. To address this question directly, we turned to a destabilized mutant of protein L that is mostly unfolded in water but can be folded upon addition of salt. We find that the effect of 200 mg/mL Dextran 20 on the folding equilibrium constant for unfolded protein L (ΔΔGU ≈ 2 kJ mol(-1)) matches the crowding effects found on the folded wild type protein and the mutant when prefolded by salt. This result indicates that the excluded volume effect is independent of starting protein stability and that crowding can shift the reaction toward the folded form when the polypeptide is in the transition region between folded and unfolded states.

Unbinding transition from fluid membranes with associated polymers

We consider two neighboring fluid membranes that are associated with long flexible polymers (proteins or other macromolecules). We are interested in two physical systems consisting of i) two adjacent membranes with end-grafted (or adsorbed) polymers (system I), or ii) two membranes confining a polymer solution (system II). In addition to the pure interactions between membranes, the presence of polymers gives rise to new induced mediated interactions, which are repulsive, for system I, and attractive, for system II. In fact, repulsive induced interactions are caused by the excluded-volume forces between grafted polymers, while attractive ones, by entropy loss, due to free motion of polymers between membranes. The main goal is a quantitative study of the unbinding transition thermodynamics that is drastically affected by the associated polymers. For system I, the repulsive polymer-mediated force delays this transition that can happen at low temperature. To investigate the unbinding phenomenon, we first present an exact mathematical analysis of the total potential that is the sum of the primitive and induced potentials. This mathematical study enables us to classify the total interaction potentials, in terms of all parameters of the problem. Second, use is made of the standard variational method to calculate the first moments of the membrane separation. Special attention is paid to the determination of the unbinding temperature. In particular, we discuss its dependence on the extra parameters related to the associated polymers, which are the surface coverage and the polymer layer thickness on each membrane (for system I) or the polymer density and the gyration radius of coils (for system II). Third, we compute the disjoining pressure upon membrane separation. Finally, we emphasize that the presence of polymers may be a mechanism to delay or to accentuate the appearance of the unbinding transition between fluid membranes.

STATISTICAL PHYSICS OF ISOTROPIC-GENESIS NEMATIC ELASTOMERS: I. STRUCTURE AND CORRELATIONS AT HIGH TEMPERATURES

Isotropic-genesis nematic elastomers (IGNEs) are liquid crystalline polymers (LCPs) that have been randomly, permanently cross-linked in the high-temperature state so as to form an equilibrium random solid. Thus, instead of being free to diffuse throughout the entire volume, as they would be in the liquid state, the constituent LCPs in an IGNE are mobile only over a finite, segment specific, length-scale controlled by the density of cross-links. We address the effects that such network-induced localization have on the liquid–crystalline characteristics of an IGNE, as probed via measurements made at high temperatures. In contrast with the case of uncross-linked LCPs, for IGNEs these characteristics are determined not only by thermal fluctuations but also by the quenched disorder associated with the cross-link constraints. To study IGNEs, we consider a microscopic model of dimer nematogens in which the dimers interact via orientation-dependent excluded volume forces. The dimers are, furthermore, randomly, permanently cross-linked via short Hookean springs, the statistics of which we model by means of a Deam–Edwards type of distribution. We show that at length-scales larger than the size of the nematogens this approach leads to a recently proposed, phenomenological Landau theory of IGNEs [Lu et al., Phys. Rev. Lett.108, 257803 (2012)], and hence predicts a regime of short-ranged oscillatory spatial correlations in the nematic alignment, of both thermal and glassy types. In addition, we consider two alternative microscopic models of IGNEs: (i) a wormlike chain model of IGNEs that are formed via the cross-linking of side-chain LCPs; and (ii) a jointed chain model of IGNEs that are formed via the cross-linking of main-chain LCPs. At large length-scales, both of these models give rise to liquid–crystalline characteristics that are qualitatively in line with those predicted on the basis of the dimer-and-springs model, reflecting the fact that the three models inhabit a common universality class.

Using Mean Field Theory to Guide Biofunctional Materials Design

AbstractCell‐instructive characteristics of extracellular matrices (ECM) resulting from a subtle balance of biomolecular and biophysical signals must be recapitulated in engineered biomaterials to facilitate regenerative therapies. However, no material explored so far allows the independent tuning of the involved molecular and physical cues due to the inherent correlation between biopolymer concentration and material properties. Addressing the resulting challenge, a rational design strategy for ECM‐inspired biohybrid hydrogels based on multi‐armed poly(ethylene glycol) and heparin, adapting a mean field approach to identify conditions at which the balance of elastic, electrostatic, and excluded volume forces results in constant heparin concentrations within swollen polymer networks with gradually varied physical properties is introduced. Applying heparin‐based biofunctionalization schemes, multiple distinct combinations of matrix parameters could be identified to effectively stimulate the pro‐angiogenic state of human endothelial cells and the differentiation of human mesenchymal stem cells. The study demonstrates the power of joint theoretical and experimental efforts in creating bioactive materials with specifically and independently controllable characteristics.

Corrected potential energy functions for constrained molecular dynamics

Atomic oscillations present in classical molecular dynamics restrict the step size that can be used. Multiple time stepping schemes offer only modest improvements, and implicit integrators are costly and inaccurate. The best approach may be to actually remove the highest frequency oscillations by constraining bond lengths and bond angles, thus permitting perhaps a 4-fold increase in the step size. However, omitting degrees of freedom produces errors in statistical averages, and rigid angles do not bend for strong excluded volume forces. These difficulties can be addressed by an enhanced treatment of holonomic constrained dynamics using ideas from papers of Fixman (1974) and Reich (1995, 1999). In particular, the 1995 paper proposes the use of “flexible” constraints, and the 1999 paper uses a modified potential energy function with rigid constraints to emulate flexible constraints. Presented here is a more direct and rigorous derivation of the latter approach, together with justification for the use of constraints in molecular modeling. With rigor comes limitations, so practical compromises are proposed: simplifications of the equations and their judicious application when assumptions are violated. Included are suggestions for new approaches.

A mixed Brownian dynamics – SPH method for the simulation of flows of suspensions of bead-spring chains in confined geometries with hydrodynamic interaction

A new coupled Brownian dynamics-smoothed particle hydrodynamics method for the computation of confined flows of non-dilute polymer solutions with full hydrodynamic interaction and excluded volume forces is presented. The starting point for the algorithm is the system of coupled Langevin equations for polymer and solvent (CLEPS) (see Oono and Freed (1981) and Öttinger and Rabin (1989), for example) describing, in the present case, the microscopic dynamics of a flowing polymer solution with a bead-spring representation of the macromolecules. Of crucial importance to the success of our numerical scheme is the manner in which bead forces are transmitted to the fluid. We adopt an approach which is reminiscent of the method of regularized Stokeslets (Cortez, 2001). Numerical tests of some two-dimensional channel flows reveal that use of a second-order projection scheme coupled with fixed SPH quadrature points leads to second-order velocity convergence and almost second-order pressure convergence, provided that the solution is sufficiently smooth. In the case of large-scale dumbbell and bead-spring chain calculations, an appropriate scaling of the number of grid points as a function of the number of beads N ensures, in the absence of excluded volume forces, that the cost of our algorithm is O( N) flops.

Calculation of the sound velocity in LiF-KBr salt mixtures with a miscibility gap

A model is proposed for an ionic melt with many kinds of ions. It uses the Debye-Huckel theory to take into account the Coulomb interaction and the van der Waals approach to consider the direct contribution of the excluded volume forces. For LiF-KBr salt melts with a miscibility gap, the immiscibility dome, density, isothermal compressibility, and the sound velocity above and below the critical mixing point are calculated. The calculation results are compared with recent experimental data.

Entropic boundary effects on the elasticity of short DNA molecules

We have measured the entropic elasticity of double-stranded-DNA molecules ranging from 247 to 1298 bp in length using axial force-clamp optical tweezers. We show that entropic end effects and excluded-volume forces from surface attachments become significant for such short molecules. The effective persistence length of the shortest molecules decreases by a factor of 2 compared to the established value for long molecules, and excluded-volume forces extend the molecules to about one third of their nominal contour length. We interpret these results in the framework of an inextensible semiflexible rod model.

The Role of Biomacromolecular Crowding, Ionic Strength, and Physicochemical Gradients in the Complexities of Life's Emergence

We have developed a general scenario of prebiotic physicochemical evolution during the Earth's Hadean eon and reviewed the relevant literature. We suggest that prebiotic chemical evolution started in microspaces with membranous walls, where external temperature and osmotic gradients were coupled to free-energy gradients of potential chemical reactions. The key feature of this scenario is the onset of an emergent evolutionary transition within the microspaces that is described by the model of complex vectorial chemistry. This transition occurs at average macromolecular crowding of 20 to 30% of the cell volume, when the ranges of action of stabilizing colloidal forces (screened electrostatic forces, hydration, and excluded volume forces) become commensurate. Under these conditions, the macromolecules divide the interior of microspaces into dynamically crowded macromolecular regions and topologically complementary electrolyte pools. Small ions and ionic metabolites are transported vectorially between the electrolyte pools and through the (semiconducting) electrolyte pathways of the crowded macromolecular regions from their high electrochemical potential (where they are biochemically produced) to their lower electrochemical potential (where they are consumed). We suggest a sequence of tentative transitions between major evolutionary periods during the Hadean eon as follows: (i) the early water world, (ii) the appearance of land masses, (iii) the pre-RNA world, (iv) the onset of complex vectorial chemistry, and (v) the RNA world and evolution toward Darwinian thresholds. We stress the importance of high ionic strength of the Hadean ocean (short Debye's lengths) and screened electrostatic interactions that enabled the onset of the vectorial structure of the cytoplasm and the possibility of life's emergence.

Laser-induced aligned self-assembly on water surfaces

The key to functionalize of engineered molecularly nanometer thick films lies in the ability to reproducibly control their structure. A number of factors influence the film morphology of self-assembled films on solid or liquid surfaces, such as the structure of the molecules/particles, wetting, solvent hydrodynamics, and evaporation. An important example is the deposition of amphiphilic molecules from a volatile solution, self-assembled onto a water surface at monolayer coverage. Upon evaporation, a myriad of microscopic two-dimensional (2D) crystallites forms a ruptured film lying in random orientation on the surface, resulting in "2D powders." Here we present a general technique, employing linearly polarized laser pulses and varying solvent composition to influence the assembly of molecules such as poly-benzyl-L-glutamate and alamethicin on water surfaces, resulting in ultrathin molecular films with aligned regions that point in the same direction, though macroscopically separated. The experimental results are tentatively explained by a mechanism that is based on excluded volume forces and "kick model" for the effect of laser pulses to induce molecular rotation that eventually results in an aligned pattern when the system is at a collective state.

Elasticity of Sub-micron DNA Molecules Studied with Axial Optical Tweezers

Understanding the elasticity of sub-micron DNA molecules is important because many crucial biological structures and processes occur on this length scale. Using optical tweezers to manipulate DNA molecules, however, is difficult when molecules are shorter than about one micron. The reason is that conventional optical tweezers stretch molecules laterally in the focal plane of the microscope objective, a mode in which steric hindrances from the coverslip and other surface effects are substantial. To overcome the problem, we developed and calibrated an axial optical tweezers that makes this length scale accessible by stretching the molecule in the axial direction of the laser beam. By varying the laser intensity, different stretching forces were applied to the DNA molecule, and the axial position of the tethered microsphere was obtained from its diffraction pattern.We measured the force-extension relationships of four short ds-DNA molecules, which are 1298 bp-, 662 bp-, 390 bp-, and 247 bp-long, using the axial optical tweezers. Using a modified worm-like chain (WLC) model for the extended DNA molecule that incorporates excluded-volume entropic effects from the coverslip and microsphere are taken into account, we obtained effective persistence lengths and excluded-volume forces for these molecules. The fitted values for the persistence length decrease with the contour length of the DNA, which is qualitatively consistent with observations by Seol et al. on longer, micron- and sub-micron sized constructs (Seol 2007). Moreover, the excluded-volume forces are close to the theoretical predictions by Segall et al (Segall 2006).

Kinetics of microphase separation in interpenetrated polymer networks in solution

We present here a theoretical study of the early kinetics of the microphase separation in crosslinked polymer blends, made of two incompatible polymers A and B, dissolved in a common good solvent. Use is made of an extended blob model used previously for the investigation of the static properties of such a transition. We are interested in the variation of the relaxation rate, tau(q), versus the wave number q, in the vicinity of the spinodal temperature. We first show that kinetics is entirely dominated by local motions, which are of Rouse type. Slow motions are absent, because of the permanent presence of crosslinks. Second, we find that the characteristic frequency, omega (q) = tau(q)(-1), increases with increasing wave number q according to a sixth power law, that is omega (q) approximately q6 phi(-9/4), where phi is the overall monomer volume fraction. Therefore, the swelling of strands due to the excluded-volume forces leads to a renormalization of the characteristic frequency by a multiplicative factor scaling as phi(-9/4). The main conclusion is that the presence of a good solvent necessitates relaxation rates less important than those relative to crosslinked mixtures in the molten state.

In-Layer Structuring of Like-Charged Macroions in a Thin Film

A thin liquid film formed from similarly charged macroions dissolved in an electrolyte solution is modeled using the canonical ensemble Monte Carlo method. Simulation studies are performed within a one-component fluid approach; i.e., the model system is composed of the macroions only but using an effective pairwise interaction that incorporates contributions from both the electrostatic nature of the supporting electrolyte and the discrete nature of a polar solvent. The layering phenomenon and in-layer ordering of the macroions in a thin macroion film are analyzed, and the role of electrostatics and excluded volume forces is discussed. We find that the electrostatic forces enhance the overall phenomenon of macroion layering while the excluded volume forces are important for the formation of the surface monolayers and contribute to the macroion structuring within monolayers.

Study of the serum albumin-polyethyleneglycol interaction to predict the protein partitioning in aqueous two-phase systems

The theoretical framework based only on the excluded volume forces is not enough to explain the bovine serum albumin partitioning behaviour in aqueous biphasic systems. The goal of this work is to look at the phase separation via the polymer effect on the water structure. Our findings suggest that polyethyleneglycol 600-protein interaction is conducted by van der Waals forces between the hydrophobic surfaces from PEG and protein molecules, which implies the rupture of hydrogen bonds from the structured water in their neighbours. Therefore, the protein will concentrate in the most water-structured phase (polyethyleneglycol) in order to reach the minimal free energy condition. When polyethyleneglycol molecular weight increases, its exclusion from protein surface prevails, thus pushing the bovine serum albumin to the bottom phase.

Osmotic force resisting chain insertion in a colloidal suspension.

We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accommodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple scaling arguments. The forces computed in these ways are shown, for nanometer chain and colloid diameters, to be of the order of tens of pN for solution volume fractions of a few tenths. These magnitudes are argued to be important for biophysical processes such as the ejection of DNA from viral capsids into the cell cytoplasm.

Effect of Solvent Quality on the Rheological and Rheooptical Properties of Flexible Polymer Solutions

The dynamics of dilute solutions of flexible polymer molecules with intramolecular excluded volume interactions are modeled using nonequilibrium Brownian dynamics (NEBD) and configuration-biased Monte Carlo (CBMC) simulations. The mathematical model consists of beads interacting through stretching and excluded volume forces under both shear and extensional flow. Various conformational and rheological quantities, such as birefringence, mean squared end-to-end distance, and viscosities, are calculated for steady-state and transient flows, with the primary independent variable being the solvent quality e*. The model predicts coil−stretch transitions in extensional flow. The molecular weight scaling of the critical extension rate is found to vary as M-1.6 under poor solvent conditions and M-2 in a good solvent, in qualitative agreement with experiments reported in the literature. Model calculations also qualitatively capture a number of other observed features, most notably higher elongational viscosities under good solvent conditions and faster relaxation behavior under poor solvent conditions.

Mode-coupling theory of self-diffusion in diblock copolymers I. General derivation and qualitative predictions

A microscopic theory of self-diffusion in diblock copolymer melts and solutions has been developed based on polymeric mode-coupling methods formulated at the level of the time and space correlated interchain excluded volume and chi-parameter forces. Equilibrium structural correlations are determined via microscopic liquid state integral equation or coarse-grained field theoretic methods. The specific dynamical consequences of self-assembly are predicted to depend rather sensitively on temperature, degree of polymerization, copolymer composition and concentration, and local block friction coefficients. The dominant physical effect for entangled diblocks is the retardation of the relaxation time of the interchain excluded volume forces due to the thermodynamically-driven segregation of blocks into microdomains, resulting in suppression of translational motion. Analytic analysis in the long chain limit allows the derivation of new scaling laws relating the self-diffusion constant and chain degree of polymerization and solution concentration. Potential limitations for real copolymer materials associated with the structurally and dynamically isotropic description adopted by the theory are discussed.