Poor Solvent Conditions Research Articles

Comparison of dissipative particle dynamics and Langevin thermostats for out-of-equilibrium simulations of polymeric systems

In this work we compare and characterize the behavior of Langevin and dissipative particle dynamics (DPD) thermostats in a broad range of nonequilibrium simulations of polymeric systems. Polymer brushes in relative sliding motion, polymeric liquids in Poiseuille and Couette flows, and brush-melt interfaces are used as model systems to analyze the efficiency and limitations of different Langevin and DPD thermostat implementations. Widely used coarse-grained bead-spring models under good and poor solvent conditions are employed to assess the effects of the thermostats. We considered equilibrium, transient, and steady state examples for testing the ability of the thermostats to maintain constant temperature and to reproduce the underlying physical phenomena in nonequilibrium situations. The common practice of switching off the Langevin thermostat in the flow direction is also critically revisited. The efficiency of different weight functions for the DPD thermostat is quantitatively analyzed as a function of the solvent quality and the nonequilibrium situation.

Macromol. Symp. 252

Cover: The present volume is based on a recent symposium held at Moscow State University in June 2006 and presents new insight on the dense state of both flexible and stiff homopolymers and copolymers in poor solvent conditions, discusses various order‐disorder phenomena and addresses also the dynamical response of polymer networks and melts.The picture on the cover is taken from the article by V. V. Vasilevskaya et al. and shows snapshots of some characteristic conformations of stiff‐chain amphiphilic macromolecules in a poor solvent.

Simulation and theory of flexible equilibrium polymers under poor solvent conditions

Grand canonical Monte Carlo simulation and simple statistical thermodynamic theory are used to model the aggregation and phase separation of systems of reversibly polymerizing monomers, capable of forming chains with or without the ability to cyclize into rings, with isotropic square-well attractions between nonbonded pairs of monomers. The general trend observed in simulation of chain-only systems, as predicted in a number of published theoretical works, is that the critical temperature for phase separation increases and the critical monomer density decreases with rising polymer bond strength. Introduction of the equilibrium between chains and rings into the theory lowers the predicted critical temperature and increases the predicted critical density. While the chain-only theories predict a vanishing critical density in the limit of complete polymerization, when ring formation is taken into account the predicted critical density in the same limit approaches the density of the onset of the ring-chain transition. The theoretically predicted effect of cyclization on chemical potential is in good qualitative agreement with a subset of simulation results in which chain-only systems were compared with equilibrium mixtures of rings and chains. The influence of attractions on the aggregation number and radius of gyration of chains and rings observed in simulations is also discussed.

Analysis of the Longitudinal Structure of a Collapsed Molecular Bottle Brush Using a Self-Consistent Field Approach

The two-gradient self-consistent field Scheutjens-Fleer (SCF-SF) approach is employed for study of conformational transition occurring in molecular bottle brushes upon decrease in the solvent strength for grafted chains. In particular, the solvent strength was varied from theta to poor solvent conditions. It was found that at moderately poor solvent strength the bottle brush collapses, keeping cylindrically uniform shape. Further decrease in the solvent strength leads to appearance of longitudinal undulations in the collapsed cylindrical structure. This result of our SCF modeling is in agreement with earlier predictions of scaling theory concerning longitudinal instability of uniform cylindrical structure of the collapsed brush. In particular, predicted by scaling theory dependence for the period of the structure on the degree of polymerization of grafted chains (∼n 1/2) and independence of the transition temperature of the molecular weight are in good agreement with results of our SCF modeling.

Molecular Dynamics Simulations of Polyelectrolyte−Polyampholyte Complexes. Effect of Solvent Quality and Salt Concentration

Complexation between polyelectrolyte and polyampholyte chains in poor solvent conditions for the polyelectrolyte backbone has been studied by molecular dynamics simulations. In a poor solvent a polyelectrolyte forms a necklace-like structure consisting of polymeric globules (beads) connected by strings of monomers. The simulation results can be explained by assuming the existence of two different mechanisms leading to the necklace formation. In the case of weak electrostatic interactions, the necklace formation is driven by optimization of short-range monomer-monomer attraction and electrostatic repulsion between charged monomers on the polymer backbone. In the case of strong electrostatic interactions, the necklace structure appears as a result of counterion condensation. While the short-range attractions between monomers are still important, the correlation-induced attraction between condensed counterions and charged monomers and electrostatic repulsion between uncompensated charges provide significant contribution to optimization of the necklace structure. Upon forming a complex with both random and diblock polyampholytes, a polyelectrolyte chain changes its necklace conformation by forming one huge bead. The collapse of the polyelectrolyte chain occurs due to the neutralization of the polyelectrolyte charge by polyampholytes. In the case of the random polyampholyte, the more positively charged sections of the chain mix with negatively charged polyelectrolyte forming the globular bead while more negatively charged chain sections form loops surrounding the collapsed core of the aggregate. In the case of diblock polyampholyte, the positively charged block, a part of the negatively charged block, and a polyelectrolyte chain form a core of the aggregate with a substantial section of the negatively charged block sticking out from the collapsed core of the aggregate. In both cases the core of the aggregate has a layered structure that is characterized by the variations in the excess of concentration of monomers belonging to polyampholyte and polyelectrolyte chains throughout the core radius. These structures appear as a result of optimization of the net electrostatic energy of the complex and short-range attractive interactions between monomers of the polyelectrolyte chain.

Equilibrium and dynamics of Langmuir monolayers when the interface is a selective solvent: Polystyrene-b-poly(t-butyl acrylate) block copolymers

The surface pressure of monolayers of insoluble diblock copolymers has been measured. One of the blocks is made of poly(t-butyl acrylate) (PtBA), and the other one by polystyrene (PS). The interface is a good solvent for PtBA, while it is a poor solvent for PS. For the sake of comparison, monolayers of a PtBA homopolymer (good solvent conditions) and of poly(4-hydroxy styrene) (P4HS) (poor solvent conditions) have been also measured. It has been found that the relative length of the blocks plays an important role on the shape of the surface pressure Pi versus surface concentration Gamma curves and also on the shape of the equilibrium compressibility versus Gamma curves. However, it does not affect the maximum value of Pi reached at high Gamma's. Surprisingly, the ellipsometric thickness of the copolymer monolayers is almost independent of the relative length of the blocks. The dynamics of the monolayers has been studied by step compression and by surface-light scattering techniques. When M(w,PtBA) >> M(w,PS) single exponential relaxations are observed. However, stretched exponentials are obtained for M(w,PS) > or = M(w,PtBA). The relaxation times decrease with increasing Gamma for all the copolymers studied. This is the behavior usually found for poor solvent conditions (P4HS) and opposite to that found for homopolymers under good solvent conditions [PtBA, poly(vinylacetate)]. This means that the solvent quality of the interface does not determine the pressure dependence of tau. The elasticity modulus of the monolayers in the kilohertz range takes values that are similar to those of the high-frequency limit of the relaxation experiments. This means that the relaxation processes have characteristic frequencies below 1 Hz.

The Swelling Behavior of Charged Hydrogels

AbstractSummary: We describe recent advances obtained in understanding the microscopic interplay of a charged hydrogel with its confined mobile counterions. Results of extensive computer simulations are compared to simple scaling descriptions for various solvent conditions. We will briefly discuss our simulation package ESPResSo which was used to perform the simulations. We demonstrate why simple scaling theories suffice to adequately describe the swelling behavior of these systems despite their enormous complexity. We will conclude with a presentation of ongoing results for polyelectrolyte networks under poor solvent conditions.

Counterion-Correlation-Induced Attraction and Necklace Formation in Polyelectrolyte Solutions: Theory and Simulations

We have developed a necklace model of hydrophobic polyelectrolytes in which the necklace structure consisting of polymeric globules (beads) connected by extended sections of the chain (strings of monomers) appears as a result of the counterion condensation and is caused by the balance of the correlation-induced attraction of condensed counterions to charged monomers and electrostatic repulsion between uncompensated charges. The size of the beads increases with polymer concentration while their number per chain decreases. We predict coexistence of necklaces with different number of beads on a polymer backbone at any polymer concentration. To test this necklace model, we performed molecular dynamics simulations of polyelectrolyte chains with degree of polymerization N varying from 25 to 373 and with fraction of charged monomers f ) 1 /3, 1 /2, and 1 in poor solvent conditions for polymer backbone. The observed concentration dependence of the bead size supports the assumption of the counterion condensation origin of the necklace structure. The overlap concentration is almost independent of the degree of polymerization for weakly charged chains (f ) 1 /3). For strongly charged chains with f ) 1 the overlap concentration follows the normal N dependence observed for polyelectrolyte solutions in £ and good solvent regimes for polymer backbone. In semidilute solutions the correlation length of fully charged chains is inversely proportional to the square root of polymer concentration. The osmotic coefficient of the solutions of polyelectrolytes in poor solvent conditions for polymer backbone exhibits nonmonotonic concentration dependence in agreement with two-zone model predictions. It decreases with increasing polymer concentration in dilute solutions, while it is an increasing function of polymer concentration in the semidilute regime. The Kratky plot of the chain form factor is in excellent agreement with the neutron scattering experiments.

Polymer solutions: from hard monomers to soft polymers

A coarse-graining strategy for dilute and semi-dilute solutions of interacting polymers, andof colloid–polymer mixtures, is briefly described. Monomer degrees of freedomare traced out to derive an effective, state-dependent pair potential between thepolymer centres of mass. The cross-over between good and poor solvent conditions isdiscussed within a scaling analysis. The method is extended to block copolymersrepresented as ‘necklaces’ of soft ‘blobs’, and its success is illustrated here in thecase of a symmetric diblock copolymer which exhibits microphase separation.

Single-Molecule AFM Study of Polystyrene Grafted at Gold Surfaces

ABSTRACT Single-molecule studies under poor solvent conditions show that atomic force microscopy (AFM) measurements of contour lengths of polystyrene 12K and 17K relate well to gel permeation chromatography (GPC) data when grafting concentrations are low (not greater than 0.7 mM). Contact angles and ellipsometry have been used to characterize the surfaces and indicate low grafting densities at this grafting concentration. Persistence lengths (p) of different length polystyrene chains, when fitted to a WLC (worm-like chain) model, show values of p = 0.23 nm±0.10 nm and p = 0.25 nm±0.13 nm, for 12 K and 17 K polystyrene, respectively, when the persistence lengths are fitted to log-normal distributions. These values are close to the expected theoretical value of 0.23 nm and further confirm that mostly single molecules were studied on these polystyrene surfaces. Higher grafting concentrations (≥1 mM) resulted in pulling multiple molecules.

Morphological variation in a toroid generated from a single polymer chain

A single semiflexible polymer chain folds into a toroidal object under poor solvent conditions. In this study, we examined the morphological change in such a toroidal state as a function of the cross-sectional area and stiffness of the chain together with the surface energy, which characterizes the segmental interaction parameter. Changes in the thickness and outer/inner radius on a toroid are interpreted in terms of these parameters. Our theoretical expectation corresponds to the actual morphological changes in a single giant DNA molecule as observed by electron microscopy.

Conductometric properties of linear polyelectrolytes in poor-solvent condition: The necklace model

We present a set of low-frequency electrical conductivity measurements of solutions of differently charged, salt-free polyelectrolytes in poor- and in good-solvent conditions, in the semidilute concentration regime. The data have been analyzed and discussed in light of the necklace model for hydrophobic polyelectrolytes recently proposed by Dobrynin et al. [Macromolecules 29, 2974 (1996)] that predicts the chains to collapse into spheroidal cores connected by narrow strings. By varying the quality of the solvent, we have measured the polyion equivalent conductance lambda(p) in an extended concentration range in the semidilute regime and have demonstrated that this parameter is influenced by the polyion chain conformation, giving further support, when the poor-solvent condition prevails, to the picture of a string of electrostatic blobs. On the contrary, in good-solvent condition, the electrical conductivity data are in reasonable good agreement with the picture of an extended chain consisting of a collection of electrostatic blobs. These electrical conductivity measurements, in light of scaling theory, furnish new experimental support for the necklace model for hydrophobic polyions in poor solvents.

Charged designed copolymers in the presence of multivalent counterions: a molecular dynamics study

We present the results of molecular dynamics simulations of charged proteinlike hydrophobic–hydrophilic (HP) copolymers in a dilute salt-free solution with multivalent counterions under poor solvent conditions. The primary sequence of these copolymers is constructed such that they can self-assemble into a segregated core–shell microstructure thus resembling some of the basic properties of globular proteins. The results are compared with those obtained earlier for the system containing monovalent counterions. The processes of coil-to-globule transition, aggregation of polyions, and counterion condensation are studied in detail as a function of temperature. The main attention is paid to the influence of the counterions of different charge on the aggregation of the copolymers. It is found that multivalent counterions considerably increase the aggregation of the chains, which form in their presence the finite-size aggregates built up from several polyions. However, the striking feature of the aggregation is that this process does not appear to lead to macroscopic phase separation. The mechanism that prevents the phase separation is discussed.

Long-time relaxation dynamics of langmuir films of a glass-forming polymer: evidence of glasslike dynamics in two dimensions.

We have carried out an experimental study on the mechanical relaxation of Langmuir films of a glass-forming polymer, poly-(4-hydroxystyrene), a good example of a two-dimensional system made of condensed polymer coils (at poor-solvent conditions). This study allows us to explore the response functions of the film and the temperature and density dependencies of the relaxation time. The dynamical properties show glasslike features (non-Debye mechanical response and non-Arrhenius relaxation times) reconcilable within the frame of the mode-coupling model.

Monte Carlo simulation of dendrimers in variable solvent quality.

We study via lattice Monte Carlo simulation and Flory theory the properties of g=1-6 dendrimers in variable solvent quality. For all the generations studied, we find that the radius of gyration R(g) collapses significantly (factor of 2) going from athermal to extreme poor solvent conditions, indicating that varying solvent quality is an effective means of controlling dendrimer size. We also find that in athermal, theta, and extreme poor solvent conditions, the radius of gyration of dendrimers scales with the total number of monomers roughly as R(g) approximately N(1/3). However, a more careful analysis shows that in athermal and theta solvents, there is, in fact, a small but systematic deviation of R(g) from R(g) approximately N(1/3) scaling and the simulation data is described better by the Flory theory prediction of R(g) approximately N(1/5)[(g+1)m](2/5) in athermal solvents and R(g) approximately N(1/4)[(g+1)m](1/4) in theta solvents. We also find for our simulation data that stronger deviations from constant density scaling are possible, with scaling behavior as shallow as R(g) approximately N(0.26) possible for solvent conditions in between theta and the completely collapsed state. It is evident therefore that dendrimers do not obey (or even approximately obey) R(g) approximately N(1/3) scaling under all solvent conditions. Under all solvent conditions, we find that the intramolecular density is dense corelike (i.e., the density maximum is in the interior of the dendrimer) and terminal groups are delocalized throughout the dendrimer.

Kinetic pathways for the collapse of semiflexible polymers

Semiflexible polymers differ from their fully flexible counterparts in that the chain has a significant stiffness. As a result in poor solvent conditions the morphology of the condensed structure is a toroidal (rather than spherical) globule. In this paper we discuss the kinetic pathways to this toroidal globule from an extended state. The two possible pathways are (i) direct wind up and (ii) a series of metastable heads. The former collapse is rapid while the later is very slow.

Polymer intrusion into narrow pores at the interface between a poor solvent and adsorbing and non-adsorbing surfaces

We report thermodynamic and conformational properties of collapsed polymer globules in a poor solvent close to adsorbing and non-adsorbing surfaces containing a cylindrical pore that is either smaller or larger than the coil size in bulk solution. Configurational Bias Monte Carlo simulations at infinite dilution were used for this purpose. We find that above the critical adsorption transition changing from good solvent to poor solvent conditions causes an increase of the partition coefficient due to cooperative monomer adsorption on the pore wall. Below the adsorption transition, the reverse effect is observed. The radius of gyration components as well as conformational (free) energies and entropies as a function of the chain centre of mass (CM) position along the pore axis reveal strong anomalies in the vicinity of the pore entrance. Below the adsorption transition, the dense globule in a poor solvent swells and deforms when penetrating the pore and recollapses once it is fully confined. Above the adsorption transition in solvents above and below the Θ-point, minima occur in the free energy at chain CM positions just in front of the pore entry causing a barrier upon pore penetration. Upon approaching the small pore from the bulk poor solvent region, the chain conformational entropy and energy run through a maximum below and above the adsorption transition.

Collective dynamics of an end-grafted polymer brush in solvents of varying quality.

The dynamic structure of a chemically end-grafted polystyrene brush bathed in solvents of varying interactions was studied by evanescent wave dynamic light scattering. It reveals distinct behavior under good and poor solvent conditions. The cooperative diffusion is a generic feature of a good solvent environment, whereas a second slow relaxation mode appears in the theta solvent regime. Its characteristics resemble self-diffusion of clusters in a gel while weak concentration fluctuations in the polymer brush decay similarly to a semidilute polymer solution.

Self-Consistent Field Theory for the Distal Ordering of Adsorbed Polymer: Comparison with the Scheutjens−Fleer Model

In a previous article (J. Chem. Phys. 2003, 119, 3483), a self-consistent field formalism was derived for weakly adsorbing polymers, valid for any chain length. It was shown that the presence of a solid wall induces an ordering of the polymers on the scale of the radius of gyration far away from the surface (the distal region). These oscillations in the polymer concentration profile were first noted in work by Semenov et al., and later observed in numerical solutions of the Scheutjens and Fleer self-consistent field model. In the present paper, we compare the weak adsorption model in more detail with the numerical results from the Scheutjens and Fleer model. Quantitative agreement is obtained for the polymer segment density profile in a good (athermal) solvent. For ϑ solvent and poor solvent conditions, it is necessary to extend the weak adsorption model to take the nonlocal character of the polymer−solvent interaction into account. Again, quantitative agreement is obtained for the polymer segment density profile, in particular for the transition from an oscillatory decaying profile to a monotonically decaying profile when the bulk polymer density is below a certain threshold value.

Cylindrical molecular brushes under poor solvent conditions: microscopic observation and scaling analysis.

Axial contraction of cylindrical molecular brushes of polymethylmethacrylate was observed by static light scattering and scanning force microscopy. Single brush molecules were visualized as worm-like particles whose length was almost three times shorter than the contour length of the backbone. A somewhat larger length was measured by light scattering in a good solvent. A scaling approach has been used to analyze the driving forces for the axial contraction and the conformation of the molecular brushes.