Jan-Michael Carrillo

Coarse-grained molecular dynamics simulations are used to probe the dynamic phenomena of polymer melts confined in nanopores. The simulation results show excellent agreement in the values obtained for the normalized coherent single chain dynamic structure factor, S(Q,Δt)/S(Q,0) . In the bulk configuration, both simulations and experiments confirm that the polymer chains follow Rouse dynamics. However, under confinement, the Rouse modes are suppressed. The mean-square radius of gyration ⟨Rg^2⟩… Show more

Coarse-grained molecular dynamics simulations are used to probe the dynamic phenomena of polymer melts confined in nanopores. The simulation results show excellent agreement in the values obtained for the normalized coherent single chain dynamic structure factor, S(Q,Δt)/S(Q,0) . In the bulk configuration, both simulations and experiments confirm that the polymer chains follow Rouse dynamics. However, under confinement, the Rouse modes are suppressed. The mean-square radius of gyration ⟨Rg^2⟩ and the average relative shape anisotropy ⟨κ^2⟩ of the conformation of the polymer chains indicate a pancake-like conformation near the surface and a bulk-like conformation near the center of the confining cylinder. This was confirmed by direct visualization of the polymer chains. Despite the presence of these different conformations, the average form factor of the confined chains still follows the Debye function which describes linear ideal chains, which is in agreement with small angle neutron scattering experiments (SANS). The experimentally inaccessible mean-square displacement (MSD) of the confined monomers, calculated as a function of radial distance from the pore surface, was obtained in the simulations. The simulations show a gradual increase of the MSD from the adsorbed, but mobile layer, to that similar to the bulk far away from the surface. Show less

Structural evolution from poly(lactide) (PLA) macromonomer to resultant PLA molecular bottlebrush during ring opening metathesis polymerization (ROMP) was investigated for the first time by combining size exclusion chromatography (SEC), small-angle neutron scattering (SANS), and coarse-grained molecular dynamics (CG-MD) simulations. Multiple aliquots were collected at various reaction times during ROMP and subsequently analyzed by SEC and SANS. These complementary techniques enable the… Show more

Structural evolution from poly(lactide) (PLA) macromonomer to resultant PLA molecular bottlebrush during ring opening metathesis polymerization (ROMP) was investigated for the first time by combining size exclusion chromatography (SEC), small-angle neutron scattering (SANS), and coarse-grained molecular dynamics (CG-MD) simulations. Multiple aliquots were collected at various reaction times during ROMP and subsequently analyzed by SEC and SANS. These complementary techniques enable the understanding of systematic changes in conversion, molecular weight and dispersity as well as structural details of PLA molecular bottlebrushes. CG-MD simulation not only predicts the experimental observations, but it also provides further insight into the analysis and interpretation of data obtained in SEC and SANS experiments. We find that PLA molecular bottlebrushes undergo three conformational transitions with increasing conversion (i.e., increasing the backbone length): (1) from an elongated to a globular shape due to longer side chain at low conversion, (2) from a globular to an elongated shape at intermediate conversion caused by excluded volume of PLA side chain, and (3) the saturation of contour length at high conversion due to chain transfer reactions. Show less

We have used small angle neutron scattering (SANS) measurement and atomistic molecular dynamics (MD) simulations to investigate the conformation of bottlebrush polymers with poly(norbornene) (PNB) backbone and different sizes of poly(lactide) (PLA) side chains (PNB25-g-PLA5, PNB25-g-PLA10, and PNB25-g-PLA19). At early stage of simulations, stretched side chains with visible spatial-correlations of about 30 Å were observed. The experimentally measured SANS data, on the other hand, does not… Show more

We have used small angle neutron scattering (SANS) measurement and atomistic molecular dynamics (MD) simulations to investigate the conformation of bottlebrush polymers with poly(norbornene) (PNB) backbone and different sizes of poly(lactide) (PLA) side chains (PNB25-g-PLA5, PNB25-g-PLA10, and PNB25-g-PLA19). At early stage of simulations, stretched side chains with visible spatial-correlations of about 30 Å were observed. The experimentally measured SANS data, on the other hand, does not exhibit any correlation peaks in the corresponding length scale indicating a compact form rather than a stretched-hairy polymer conformation. As the simulation continued, the spatial correlations between side chains disappeared after about 40 ns of chain relaxation, and the scattering intensity calculated for the simulated structure becomes reasonably close to the measured one. Statistical approach is used to overcome the time scale limitation and search for optimal conformation space, which also provides a good agreement with the experimental data. Further coarse-grained simulation results suggest that the side chain conformation strongly depends on the solubility competition among side chain, backbone, and solvent. Significant changes of backbone dynamics due to the side chain encapsulation have been revealed and discussed. Show less

We present results of the hybrid Monte Carlo/molecular dynamics simulations of the osmotic pressure of salt solutions of polyelectrolytes. In our simulations, we used a coarse-grained representation of polyelectrolyte chains, counterions and salt ions. During simulation runs, we alternate Monte Carlo and molecular dynamics simulation steps. Monte Carlo steps were used to perform small ion exchange between simulation box containing salt ions (salt reservoir) and simulation box with… Show more

We present results of the hybrid Monte Carlo/molecular dynamics simulations of the osmotic pressure of salt solutions of polyelectrolytes. In our simulations, we used a coarse-grained representation of polyelectrolyte chains, counterions and salt ions. During simulation runs, we alternate Monte Carlo and molecular dynamics simulation steps. Monte Carlo steps were used to perform small ion exchange between simulation box containing salt ions (salt reservoir) and simulation box with polyelectrolyte chains, counterions and salt ions (polyelectrolyte solution). This allowed us to model Donnan equilibrium and partitioning of salt and counterions across membrane impermeable to polyelectrolyte chains. Our simulations have shown that the main contribution to the system osmotic pressure is due to salt ions and osmotically active counterions. The fraction of the condensed (osmotically inactive) counterions first increases with decreases in the solution ionic strength then it saturates. The reduced value of the system osmotic coefficient is a universal function of the ratio of the concentration of osmotically active counterions and salt concentration in salt reservoir. Simulation results are in a very good agreement with osmotic pressure measurements in sodium polystyrene sulfonate, DNA, polyacrylic acid, sodium polyanetholesulfonic acid, polyvinylbenzoic acid, and polydiallyldimethylammonium chloride solutions. Show less

We present a general strategy for enabling reversible shape transformation in semicrystalline shape memory (SM) materials, which integrates three different SM behaviors: conventional one-way SM, two-way reversible SM, and one-way reversible SM. While two-way reversible shape memory (RSM) is observed upon heating and cooling cycles, the one-way RSM occurs upon heating only. Shape reversibility is achieved through partial melting of a crystalline scaffold which secures memory of a temporary shape… Show more

We present a general strategy for enabling reversible shape transformation in semicrystalline shape memory (SM) materials, which integrates three different SM behaviors: conventional one-way SM, two-way reversible SM, and one-way reversible SM. While two-way reversible shape memory (RSM) is observed upon heating and cooling cycles, the one-way RSM occurs upon heating only. Shape reversibility is achieved through partial melting of a crystalline scaffold which secures memory of a temporary shape by leaving a latent template for recrystallization. This behavior is neither mechanically nor structurally constrained, thereby allowing for multiple switching between encoded shapes without applying any external force, which was demonstrated for different shapes including hairpin, coil, origami, and a robotic gripper. Fraction of reversible strain increases with cross-linking density, reaching a maximum of ca. 70%, and then decreases at higher cross-linking densities. This behavior has been shown to correlate with efficiency of securing the temporary shape. Show less

The ability of liquid crystal (LC) molecules to respond to changes in their environment makes them an interesting candidate for thin film applications, particularly in bio-sensing, bio-mimicking devices, and optics. Yet the understanding of the (in)stability of this family of thin films has been limited by the inherent challenges encountered by experiment and continuum models. Using unprecedented large-scale molecular dynamics (MD) simulations, we address the rupture origin of LC thin films… Show more

The ability of liquid crystal (LC) molecules to respond to changes in their environment makes them an interesting candidate for thin film applications, particularly in bio-sensing, bio-mimicking devices, and optics. Yet the understanding of the (in)stability of this family of thin films has been limited by the inherent challenges encountered by experiment and continuum models. Using unprecedented large-scale molecular dynamics (MD) simulations, we address the rupture origin of LC thin films wetting a solid substrate at length scales similar to those in experiment. Our simulations show the key signatures of spinodal instability in isotropic and nematic films on top of thermal nucleation, and importantly, for the first time, evidence of a common rupture mechanism independent of initial thickness and LC orientational ordering. We further demonstrate that the primary driving force for rupture is closely related to the tendency of the LC mesogens to recover their local environment in the bulk state. Our study not only provides new insights into the rupture mechanism of liquid crystal films, but also sets the stage for future investigations of thin film systems using peta-scale molecular dynamics simulations. Show less

Organic photovoltaics (OPVs) are topic of extensive research for their potential application in solar cells. Recent work has led to the development of a coarse-grained model for studying poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) blends with molecular simulations. Here we provide further validation of the force field and use it to study the thermal annealing process of P3HT:PCBM blends. A key finding of our study is that, in contrast to a previous… Show more

Organic photovoltaics (OPVs) are topic of extensive research for their potential application in solar cells. Recent work has led to the development of a coarse-grained model for studying poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) blends with molecular simulations. Here we provide further validation of the force field and use it to study the thermal annealing process of P3HT:PCBM blends. A key finding of our study is that, in contrast to a previous report, the annealing process does not converge at the short time scales reported. Rather, we find that the self assembly of the blends is characterized by three rate dependent stages that require much longer simulations to approach convergence. Using state-of-the- art high performance computing, we are able to study annealing at length and time scales commensurate with devices used in experiments. Our simulations show different phase segregated morphologies dependent on the P3HT chain length and PCBM volume fraction in the blend. For short chain lengths, we observed a smectic morphology containing alternate P3HT and PCBM domains. In contrast, a phase segregated morphology containing domains of P3HT and PCBM distributed randomly in space is found for longer chain lengths. Theoretical arguments justifying stabilization of these morphologies due to shape anisotropy of P3HT (rod-like) and PCBM (sphere-like) are presented. Furthermore, results on structure factor, miscibility of P3HT and PCBM, domain spacing and kinetics of phase segregation in the blends are presented in detail. Qualitative comparison of these results with small-angle neutron scattering experiments from literature is presented and an excellent agreement is found. Show less

Numerous issues have disrupted the trend for increasing computational performance with faster CPU clock frequencies. In order to exploit the potential performance of new computers, it is becoming increasingly desirable to re-evaluate computational physics methods and models with an eye toward approaches that allow for increased concurrency and data locality. The evaluation of long-range Coulombic interactions is a common bottleneck for molecular dynamics simulations. Enhanced truncation… Show more

Numerous issues have disrupted the trend for increasing computational performance with faster CPU clock frequencies. In order to exploit the potential performance of new computers, it is becoming increasingly desirable to re-evaluate computational physics methods and models with an eye toward approaches that allow for increased concurrency and data locality. The evaluation of long-range Coulombic interactions is a common bottleneck for molecular dynamics simulations. Enhanced truncation approaches have been proposed as an alternative method and are particularly well-suited for many-core architectures and GPUs due to the inherent fine-grain parallelism that can be exploited. In this paper, we compare efficient truncation-based approximations to evaluation of electrostatic forces with the more traditional particle–particle particle-mesh (P3M) method for the molecular dynamics simulation of polyelectrolyte brush layers. We show that with the use of GPU accelerators, large parallel simulations using P3M can be greater than 3 times faster due to a reduction in the mesh-size required. Alternatively, using a truncation-based scheme can improve performance even further. This approach can be up to 3.9 times faster than GPU-accelerated P3M for many polymer systems and results in accurate calculation of shear velocities and disjoining pressures for brush layers. For configurations with highly nonuniform charge distributions, however, we find that it is more efficient to use P3M; for these systems, computationally efficient parametrizations of the truncation-based approach do not produce accurate counterion density profiles or brush morphologies. Show less

Applications requiring pristine graphene derived from graphite demand a solution stabilization method that utilizes an easily removable media. Using a combination of molecular dynamics simulations and experimental techniques, we investigate the solublization/suspension of pristine graphene sheets by an equimolar mixture of benzene and hexafluorobenzene (C6H6/C6F6) that is known to form an ordered structure solidifying at 23.7 °C. Our simulations show that the graphene surface templates the… Show more

Applications requiring pristine graphene derived from graphite demand a solution stabilization method that utilizes an easily removable media. Using a combination of molecular dynamics simulations and experimental techniques, we investigate the solublization/suspension of pristine graphene sheets by an equimolar mixture of benzene and hexafluorobenzene (C6H6/C6F6) that is known to form an ordered structure solidifying at 23.7 °C. Our simulations show that the graphene surface templates the self-assembly of the mixture into periodic layers extending up to 30 Å from both sides of the graphene sheet. The solvent structuring is driven by quadrupolar interactions and consists of stacks of alternating C6H6/C6F6 molecules rising from the surface of the graphene. These stacks result in density oscillations with a period of about 3.4 Å. The high affinity of the 1:1 C6H6/C6F6 mixture with graphene is consistent with observed hysteresis in Wilhelmy plate measurements using highly ordered pyrolytic graphite (HOPG). AFM, SEM, and TEM techniques verify the state of the suspended material after sonication. As an example of the utility of this mixture, graphene suspensions are freeze-dried at room temperature to produce a sponge-like morphology that reflects the structure of the graphene sheets in solution. Show less

We present results of the molecular dynamics simulations of salt solutions of polyelectrolyte chains with number of monomers N = 300. Polyelectrolyte solutions are modeled as an ensemble of bead–spring chains of charged Lennard-Jones particles with explicit counterions and salt ions. Our simulations show that in dilute and semidilute polyelectrolyte solutions the electrostatic induced chain persistence length scales with the solution ionic strength as I–1/2. This dependence of the chain… Show more

We present results of the molecular dynamics simulations of salt solutions of polyelectrolyte chains with number of monomers N = 300. Polyelectrolyte solutions are modeled as an ensemble of bead–spring chains of charged Lennard-Jones particles with explicit counterions and salt ions. Our simulations show that in dilute and semidilute polyelectrolyte solutions the electrostatic induced chain persistence length scales with the solution ionic strength as I–1/2. This dependence of the chain persistence length is due to counterion condensation on the polymer backbone. In dilute polyelectrolyte solutions the chain size decreases with increasing the salt concentration as R I–1/5. This is in agreement with the scaling of the chain persistence length on the solution ionic strength, lp I–1/2. In semidilute solution regime at low salt concentrations the chain size decreases with increasing polymer concentration, R cp–1/4, while at high salt concentrations we observed a weaker dependence of the chain size on the solution ionic strength, R I–1/8. Our simulations also confirmed that the peak position in the polymer scattering function scales with the polymer concentration in dilute polyelectrolyte solutions as cp1/3. In semidilute polyelectrolyte solutions at low salt concentrations the location of the peak in the scattering function shifts toward the large values of q* cp1/2 while at high salt concentrations the peak location depends on the solution ionic strength as I–1/4. Analysis of the simulation data throughout the studied salt and polymer concentration ranges shows that there exist general scaling relations between multiple quantities X(I) in salt solutions and corresponding quantities X(I0) in salt-free solutions, X(I) = X(I0)(I/I0)β. The exponent β = −1/2 for chain persistence length lp, β = 1/4 for solution correlation length ξ, and β = −1/5 and β = −1/8 for chain size R in dilute and semidilute solution regimes, respectively. Show less

We perform molecular dynamics simulations on the detachment of nanoparticles from a substrate. The critical detachment force, f*, is obtained as a function of the nanoparticle radius, Rp, shear modulus, G, surface energy, γp, and work of adhesion, W. The magnitude of the detachment force is shown to increase from πWRp to 2.2πWRp with increasing nanoparticle shear modulus and nanoparticle size. This variation of the detachment force is a manifestation of neck formation upon nanoparticle… Show more

We perform molecular dynamics simulations on the detachment of nanoparticles from a substrate. The critical detachment force, f*, is obtained as a function of the nanoparticle radius, Rp, shear modulus, G, surface energy, γp, and work of adhesion, W. The magnitude of the detachment force is shown to increase from πWRp to 2.2πWRp with increasing nanoparticle shear modulus and nanoparticle size. This variation of the detachment force is a manifestation of neck formation upon nanoparticle detachment. Using scaling analysis, we show that the magnitude of the detachment force is controlled by the balance of the nanoparticle elastic energy, neck surface energy, and energy of nanoparticle adhesion to a substrate. It is a function of the dimensionless parameter δ γp(GRp)−1/3W–2/3, which is proportional to the ratio of the surface energy of a neck and the elastic energy of a deformed nanoparticle. In the case of small values of the parameter δ 1, the critical detachment force approaches a critical Johnson, Kendall, and Roberts force, f* ≈ 1.5πWRp, as is usually the case for strongly cross-linked, large nanoparticles. However, in the opposite limit, corresponding to soft small nanoparticles for which δ1, the critical detachment force, f*, scales as f* γp3/2Rp1/2G–1/2. Simulation data are described by a scaling function f*γp3/2Rp1/2G–1/2δ–1.89. Show less

We performed molecular dynamics simulations of a multilayer assembly of oppositely charged nanoparticles on porous substrates with cylindrical pores. The film was constructed by sequential adsorption of oppositely charged nanoparticles in layer-by-layer fashion from dilute solutions. The multilayer assembly proceeds through surface overcharging after completion of each deposition step. There is almost linear growth in the surface coverage and film thickness during the deposition process. The… Show more

We performed molecular dynamics simulations of a multilayer assembly of oppositely charged nanoparticles on porous substrates with cylindrical pores. The film was constructed by sequential adsorption of oppositely charged nanoparticles in layer-by-layer fashion from dilute solutions. The multilayer assembly proceeds through surface overcharging after completion of each deposition step. There is almost linear growth in the surface coverage and film thickness during the deposition process. The multilayer assembly also occurs inside cylindrical pores. The adsorption of nanoparticles inside pores is hindered by the electrostatic interactions of newly adsorbing nanoparticles with the multilayer film forming inside the pores and on the substrate. This is manifested in the saturation of the average thickness of the nanoparticle layers formed on the pore walls with an increasing number of deposition steps. The distribution of nanoparticles inside the cylindrical pore was nonuniform with a significant excess of nanoparticles at the pore entrance. Show less

Using molecular dynamics simulations and theoretical analysis we studied dynamics of a bottlebrush macromolecule in a matrix of linear chains under flow conditions. Our simulations showed that the velocity of a bottlebrush depends on the degree of polymerization of the brush backbone, degree of polymerization of the side chains and degree of polymerization of the linear chains. The velocity of a bottlebrush, first, decreases with increasing the bottlebrush degree of polymerization then it… Show more

Using molecular dynamics simulations and theoretical analysis we studied dynamics of a bottlebrush macromolecule in a matrix of linear chains under flow conditions. Our simulations showed that the velocity of a bottlebrush depends on the degree of polymerization of the brush backbone, degree of polymerization of the side chains and degree of polymerization of the linear chains. The velocity of a bottlebrush, first, decreases with increasing the bottlebrush degree of polymerization then it saturates. The location of the saturation regime was shown to be a universal function of the bottlebrush area. This behavior was explained by a combined effect of the hydrodynamic drag acting on a bottlebrush macromolecule from the matrix of faster moving linear chains and by the difference in the friction coefficients of a bottlebrush macromolecule and of linear chains with a substrate. A proposed theoretical model of bottlebrush dynamics under flow conditions is in a good agreement with simulation results Show less

Networks and gels are part of our everyday experience starting from automotive tires and rubber bands to biological tissues and cells. Biological and polymeric networks show remarkably high deformability at relatively small stresses and can sustain reversible deformations up to 10 times their initial size. A distinctive feature of these materials is highly nonlinear stress−strain curves leading to material hardening with increasing deformation. This differentiates networks and gels from… Show more

Networks and gels are part of our everyday experience starting from automotive tires and rubber bands to biological tissues and cells. Biological and polymeric networks show remarkably high deformability at relatively small stresses and can sustain reversible deformations up to 10 times their initial size. A distinctive feature of these materials is highly nonlinear stress−strain curves leading to material hardening with increasing deformation. This differentiates networks and gels from conventional materials, such as metals and glasses, showing linear stress−strain relationship in the reversible deformation regime. Using theoretical analysis and molecular dynamics simulations, we propose and test a theory that describes nonlinear mechanical properties of a broad variety of biological and polymeric networks and gels by relating their macroscopic strain-hardening behavior with molecular parameters of the network strands. This theory provides a universal relationship between the strain-dependent network modulus and the network deformation and explains strain-hardening of natural rubber, synthetic polymeric networks, and biopolymer networks of actin, collagen, fibrin, vimentin, and neurofilaments. Show less

Using molecular dynamics simulations, we study the effect of the brush grafting density and degree of polymerization of the side chains on conformations of brush layers made of charged bottle-brush macromolecules. The thickness of the brush layer first decreases with increasing brush grafting density; then, it saturates and remains constant in the wide interval of the brush grafting densities. The brush layers consisting of the bottle-brush macromolecules with longer side chains have a larger… Show more

Using molecular dynamics simulations, we study the effect of the brush grafting density and degree of polymerization of the side chains on conformations of brush layers made of charged bottle-brush macromolecules. The thickness of the brush layer first decreases with increasing brush grafting density; then, it saturates and remains constant in the wide interval of the brush grafting densities. The brush layers consisting of the bottle-brush macromolecules with longer side chains have a larger layer thickness. The elongation of the side chains of the bottle-brush macromolecules decreases with increasing brush grafting density. This contraction of the side chains is due to counterion condensation inside the volume occupied by bottle-brushes. Our simulations showed that counterion condensation is a multiscale process reflecting different symmetries of the bottle-brush layer. Show less

The mechanical response of networks, gels, and brush layers is a manifestation of the elastic properties of the individual macromolecules. Furthermore, the elastic response of macromolecules to an applied force is the foundation of the single-molecule force spectroscopy techniques. The two main classes of models describing chain elasticity include the worm-like and freely jointed chain models. The selection between these two classes of models is based on the assumptions about chain flexibility.… Show more

The mechanical response of networks, gels, and brush layers is a manifestation of the elastic properties of the individual macromolecules. Furthermore, the elastic response of macromolecules to an applied force is the foundation of the single-molecule force spectroscopy techniques. The two main classes of models describing chain elasticity include the worm-like and freely jointed chain models. The selection between these two classes of models is based on the assumptions about chain flexibility. In many experimental situations, the choice is not clear, and a model describing the crossover between these two limiting classes is therefore in high demand. We are proposing a unified chain deformation model that describes the force−deformation curve in terms of the chain bending constant, K, and bond length, b. This model demonstrates that the worm-like and freely jointed chain models correspond to two different regimes of polymer deformation, and the crossover between these two regimes depends on the chain bending rigidity and the magnitude of the applied force. Polymer chains with bending constant K > 1 behave as a worm-like chain under tension in the interval of the applied forces f ≤ KkBT/b and as a freely jointed chain for f ≥ KkBT/b. (kB is the Boltzmann constant and T is the absolute temperature.) The proposed crossover expression for chain deformation is in excellent agreement with the results of the molecular dynamics simulations of chain deformation and single-molecule deformation experiments of biological and synthetic macromolecules. Show less

We have developed a new model of nanoparticle adhesion which explicitly takes into account the change in the nanoparticle surface energy. Using combination of the molecular dynamics simulations and theoretical calculations we have showed that the deformation of the adsorbed nanoparticles is a function of the dimensionless parameter β γp(GRp)−2/3W−1/3, where G is the particle shear modulus, Rp is the initial particle radius, γp is the polymer interfacial energy, and W is the particle work of… Show more

We have developed a new model of nanoparticle adhesion which explicitly takes into account the change in the nanoparticle surface energy. Using combination of the molecular dynamics simulations and theoretical calculations we have showed that the deformation of the adsorbed nanoparticles is a function of the dimensionless parameter β γp(GRp)−2/3W−1/3, where G is the particle shear modulus, Rp is the initial particle radius, γp is the polymer interfacial energy, and W is the particle work of adhesion. In the case of small values of the parameter β < 0.1, which is usually the case for strongly cross-linked large nanoparticles, the particle deformation can be described in the framework of the classical Johnson, Kendall, and Roberts (JKR) theory. However, we observed a significant deviation from the classical JKR theory in the case of the weakly cross-linked nanoparticles that experience large shape deformations upon particle adhesion. In this case the interfacial energy of the nanoparticle plays an important role controlling nanoparticle deformation. Our model of the nanoparticle adhesion is in a very good agreement with the simulation results and provides a new universal scaling relationship for nanoparticle deformation as a function of the system parameters. Show less

Hydrophobic polyelectrolytes are known to form necklace-like structures of dense beads connected by strings of monomers. This structure appears as a result of optimization of the electrostatic and short-range interactions. To elucidate the effect of counterion condensation and solvent on polyelectrolyte conformations, we performed two sets of molecular dynamics simulations of model poly(styrene)-co-styrene sodium sulfonate (NaPSS) chains with the degree of polymerization N = 16−64 and fraction… Show more

Hydrophobic polyelectrolytes are known to form necklace-like structures of dense beads connected by strings of monomers. This structure appears as a result of optimization of the electrostatic and short-range interactions. To elucidate the effect of counterion condensation and solvent on polyelectrolyte conformations, we performed two sets of molecular dynamics simulations of model poly(styrene)-co-styrene sodium sulfonate (NaPSS) chains with the degree of polymerization N = 16−64 and fraction of charged monomers f = 0.25−1 in aqueous solutions: (1) water molecules were considered explicitly using the TIP3P-PME model and (2) water molecules were modeled as a dielectric continuum with the dielectric constant 77.73. Our simulations showed that with increasing fraction of sulfonated groups f a polystyrene sulfonate chain adopts an elongated conformation. There is a transition between collapsed and elongated states which is manifested in the change of the scaling dependence of the chain size on the degree of polymerization. The effect of the water−ion interactions on counterion condensation was analyzed by comparing the radial distribution functions between the sulfonated groups and counterions for chains with different f values. In the case of the collapsed NaPSS chains, it was found that ionized groups are located at the globular surface Show less

Using combination of the molecular dynamics simulations and theoretical calculations, we have demonstrated that the bending rigidity of biological polyelectrolytes (semiflexible charged polymers) is force dependent. The effective chain bending rigidity decreases with increasing the value of the applied force. At small and intermediate values of the applied forces a semiflexible polyelectrolyte chain behaves similar to a neutral chain with the effective bending rigidity equal to the sum of the… Show more

Using combination of the molecular dynamics simulations and theoretical calculations, we have demonstrated that the bending rigidity of biological polyelectrolytes (semiflexible charged polymers) is force dependent. The effective chain bending rigidity decreases with increasing the value of the applied force. At small and intermediate values of the applied forces a semiflexible polyelectrolyte chain behaves similar to a neutral chain with the effective bending rigidity equal to the sum of the bare chain bending rigidity and electrostatic bending rigidity which has a well-known Odijk−Skolnick−Fixman (OSF) form with a quadratic dependence on the Debye radius. However, at large values of the applied force when the magnitude of the external force exceeds an electrostatic force responsible for the local chain stretching the effective chain bending rigidity is controlled by the bare chain elastic properties. This dependence of the bending rigidity on the applied force is a result of the scale dependent effect of the electrostatic interactions on the chain bending properties that can be approximated by two characteristic length scales. One describes the chain’s elasticity at the distances along the polymer backbone shorter than the Debye screening length while another controls the long-scale chain’s orientational correlations. By applying an external force to a semiflexible polyelectrolyte chain one probes different chain’s deformation modes. Simulation results and theoretical model demonstrate a good quantitative agreement. Show less

We have performed coarse-grained molecular dynamics simulations of molding and replication of nanometer-size objects. Nanoimprinting of hemispherical particles was modeled as a three-step process: (1) a mold was created by pressing a hard hemispherical particle (master template) into a polymeric film; (2) a polymeric film was cross-linked fixing a negative image of a master mold into a polymeric film; (3) a polymeric mold was pressed into a monomeric liquid replicating an original master. The… Show more

We have performed coarse-grained molecular dynamics simulations of molding and replication of nanometer-size objects. Nanoimprinting of hemispherical particles was modeled as a three-step process: (1) a mold was created by pressing a hard hemispherical particle (master template) into a polymeric film; (2) a polymeric film was cross-linked fixing a negative image of a master mold into a polymeric film; (3) a polymeric mold was pressed into a monomeric liquid replicating an original master. The quality of the replication process was analyzed by comparing the shape of the replica with the shape of the master. It is shown that deformation of a polymeric stamp during the replication process (Step 3) is a result of optimization of the surface energy of the mold−liquid interface and the elastic energy of the polymeric mold. The relative deformation, ε, of the replica is a function of the universal parameter γ/(GR0), where γ is the surface energy of the polymer−liquid interface, G is the shear modulus of the polymer network, and R0 is the radius of the master. In the case of small deformations, this function reduces to ε γ/(GR0). Show less

Using molecular dynamics simulations and scaling analysis, we study the effect of the solvent quality for the polymer backbone, the strength of the electrostatic interactions, the chain degree of polymerization, and the brush grafting density on conformations of the planar polyelectrolyte brushes in salt-free solutions. Polyelectrolyte brush forms: (1) vertically oriented cylindrical aggregates (bundles of chains), (2) maze-like aggregate structures, or (3) thin polymeric layer covering a… Show more

Using molecular dynamics simulations and scaling analysis, we study the effect of the solvent quality for the polymer backbone, the strength of the electrostatic interactions, the chain degree of polymerization, and the brush grafting density on conformations of the planar polyelectrolyte brushes in salt-free solutions. Polyelectrolyte brush forms: (1) vertically oriented cylindrical aggregates (bundles of chains), (2) maze-like aggregate structures, or (3) thin polymeric layer covering a substrate. These different brush morphologies appear as a result of the fine interplay between electrostatic and short-range monomer−monomer interactions. The brush thickness shows nonmonotonic dependence on the value of the Bjerrum length. It first increases with the increasing value of the Bjerrum length, and then it begins to decrease. This behavior is a result of counterion condensation within a brush volume. Show less

Using molecular dynamics simulations in combination with scaling analysis, we have studied the effects of the solvent quality and the strength of the electrostatic interactions on the conformations of spherical polyelectrolyte brushes in salt-free solutions. The spherical polyelectrolyte brush could be in one of four conformations: (1) a star-like conformation, (2) a “star of bundles” conformation in which the polyelectrolyte chains self-assemble into pinned cylindrical micelles, (3) a… Show more

Using molecular dynamics simulations in combination with scaling analysis, we have studied the effects of the solvent quality and the strength of the electrostatic interactions on the conformations of spherical polyelectrolyte brushes in salt-free solutions. The spherical polyelectrolyte brush could be in one of four conformations: (1) a star-like conformation, (2) a “star of bundles” conformation in which the polyelectrolyte chains self-assemble into pinned cylindrical micelles, (3) a micelle-like conformation with a dense core and charged corona, or (4) a conformation in which there is a thin polymeric layer uniformly covering the particle surface. These different brush conformations appear as a result of the fine interplay between electrostatic and monomer−monomer interactions. The brush thickness depends nonmonotonically on the value of the Bjerrum length. This dependence of the brush thickness is due to counterion condensation inside the brush volume. We have also established that bundle formation in poor solvent conditions for the polymer backbone can also occur in a planar polyelectrolyte brush. In this case, the grafted polyelectrolyte chains form hemispherical aggregates at low polymer grafting densities, cylindrical aggregates at an intermediate range of the grafting densities, and vertically oriented ribbon-like aggregates at high grafting densities. Show less