Conformation of a polymer chain in solution: an exact density expansion approach

The conformation of a polymer chain in solution is intrinsically coupled to the thermodynamic and structural properties of the solvent. Here we study such solvent effects in a system consisting of a flexible interaction-site n-mer chain immersed in a monomeric solvent. Chain conformation is described with a set of intramolecular site-site probability functions. We derive an exact density expansion for these intramolecular probability functions and give a diagrammatic representation of the terms contributing at each order of the expansion. The expansion is tested for a short hard-sphere chain (n=3 or 4) with site diameter sigma in a hard-sphere solvent with solvent diameter D. In comparison with Monte Carlo simulation results for 0.2< or =D/sigma< or =100, the expansion (taken to second order) is found to be quantitatively accurate for low to moderate solvent volume fractions for all size ratios. Average chain dimensions are predicted accurately up to liquidlike solvent densities. The hard-sphere chains are compressed with both increasing solvent density and decreasing solvent size. For small solvent (D相似文献   

Equilibrium conformational dynamics of a polymer in a solvent

Molecular dynamics simulations were used to study the conformational dynamics of a bead-spring model polymer in an explicit solvent under good solvent conditions. The dynamics of the polymer chain were investigated using an analysis of the time autocorrelation functions of the Rouse coordinates of the polymer chain. We have investigated the variation of the correlation functions with polymer chain length N, solvent density rho, and system size. The measured initial decay rates gamma(p) of the correlation functions were compared with the predictions from a theory of polymer dynamics which uses the Oseen tensor to describe hydrodynamic interactions between monomers. Over the range of chain lengths considered (N = 30-60 monomers), the predicted scaling of gamma(p) proportional to N(-3nu) was observed at high rho, where nu is the polymer scaling exponent. The predicted gamma(p) are generally higher than the measured values. This discrepancy increases with decreasing rho, as a result in the breakdown in the conditions required for the Oseen approximation. The agreement between theory and simulation at high rho improves considerably if the theoretical expression for gamma(p) is modified to avoid sum-to-integral approximations, and if the values of (R(p)2), which are used in the theory, are taken directly from the simulation rather than being calculated using approximate scaling relations. The observed finite-size scaling of gamma(p) is not quantitatively consistent with the theoretical predictions.     

Unforced translocation of a polymer chain through a nanopore: the solvent effect

The authors have performed the Langevin dynamics simulation to investigate the unforced polymer translocation through a narrow nanopore in an impermeable membrane. The effects of solvent quality controlled by the attraction strength lambda of the Lennard-Jones cosine potential between polymer beads and beads on two sides of the membrane on the translocation processes are extensively examined. For polymer translocation under the same solvent quality on both sides of the membrane, the two-dimensional and three-dimensional simulations confirm the scaling law of tautrans approximately N1+2upsilon for the translocation in the good solvent, where tautrans is the translocation time, N is the chain length, and upsilon is the Flory exponent. For the three-dimensional polymer translocation under different solvent qualities on two sides of the membrane, the translocation efficiency may be notably improved. The scaling law between tautrans and N varies from tautrans approximately N1+2upsilon to tautrans approximately N with the increase of the difference of solvent qualities, and the crossover occurs at the theta temperature point, where a scaling law of tautrans approximately N1.27 is found. The simulation results here also show that the translocation time changes from a wide and asymmetric distribution with a long tail to a narrow and symmetric distribution with the increase of the difference of the solvent qualities.     

Lois d'échelles dans les interfaces couvertes de polymères

In this note, we adress the problem of theoretically describing interfaces covered with long polymer chains. The usual observable for this problem is the monomer volume fraction, , as a function of the distance from the surface, z. However, this function is not always relevant. For example, when the interface is made of a strongly attached polymer chain in the absence of any solvent: the -profile is flat and does not give us any insight into the intimate organization of the layer. We suggest that the function S, defined e.g. as an integral of the loop size distribution, is a powerful tool. In particular, we use this function S and straightforward scaling arguments to recover two important results concerning reversibly and irreversibly adsorbed polymer layers.     

Transport properties in concentrated polymer solutions

Transport properties of polymer solutions at finite concentration are derived in the partial draining case by formulating a static version of the theory given by Freed and Edwards (FE) for unentangled concentrated polymer solution. The method follows the Kirkwood—Riseman theory for infinitely dilute solutions: the dynamics of the polymer are ignored apart from the overall rotation or translation of the chain and the solvent velocity is given by the Navier—Stokes equations perturbed by point friction forces. The concentration dependence of viscosity and translational friction coefficient of finite chains obtained by numerical calculations are compared with the results of the FE closed-form solution. It is shown that the screening of the hydrodynamic interaction approximately follows Debye-like behavior in the entire range of concentration. The progressive balancing of the increasing intramolecular hydrodynamic interaction with its reduction due to the screening effects, as the molecular weight increases, is well evidenced by comparing results obtained at constant number concentration for different chain lengths.     

Molecular dynamics study of the methanol effect on the membrane morphology of perfluorosulfonic ionomers

The membranes of a perfluorosulfonic acid polymer swollen in 10-80 wt % methanol solution were investigated to elucidate the methanol effect on their morphologies, such as size of the solvent cluster, solvent location, and polymer structure, by using isothermal-isobaric molecular dynamics simulations. In higher methanol concentrations, we found less-spherical solvent aggregation and a more spread polymer structure because of the ampholytic nature of methanol. The partial radial distribution functions between solvent oxygen and fluorocarbons, which are composed of the main chain, clearly show that methanol is located closer to the polymer matrix than water. On the other hand, water is preferentially located in the vicinity of an acidic headgroup, SO(3)(-), compared with methanol, although both have similar attractive interaction energies to the acidic group. Furthermore, we discussed solvent dynamics and hydrogen bonding between sulfonic oxygen and solvent O-H groups.     

Strongly stretched polymer brushes

Polymer “brushes” are formed when long-chain molecules are somehow attached by one end at an interface with a relatively small area per chain. Such adsorbed brushes in the presence of solvent may be used to modify surface properties, stabilize colloidal particles, etc. Strongly segregated block copolymer phases, or interfacial layers of such “polymeric surfactants” may also be modeled in terms of “melt brushes,” (i.e., brushes without solvent). In both cases, when chain attachments are crowded on the interface, the chains stretch out to avoid neighboring chains. The resulting physical state has properties markedly different from polymer solutions, gels, or weakly adsorbed polymer layers. When the chains are strongly stretched, their statistical mechanics become simpler, as fluctuations around the set of most probable conformations are suppressed. This makes possible many pencil-and-paper calculations of brush properties, including bending and compressional moduli, and detailed knowledge of the chain conformations. As a recent example, I will describe calculations of phase diagrams of strongly segregated block copolymers including bicontinuous double-diamond phases. © 1994 John Wiley & Sons, Inc.     

On the curvature dependence of the interfacial tension in a symmetric three-component interface

We consider a symmetric interface between two polymers A(N) and B(N) in a common monomeric solvent S using the mean-field Scheutjens-Fleer self-consistent field theory and focus on the curvature dependence of the interfacial tension. In multi-component systems there is not one unique scenario to curve such an interface. We elaborate on this by keeping either the chemical potential of the solvent or the bulk concentration of the solvent fixed, that is we focus on the semi-grand canonical ensemble case. Following Helfrich, we expand the surface tension as a Taylor series in the curvature parameters and find that there is a non-zero linear dependence of the interfacial tension on the mean curvature in both cases. This implies a finite Tolman length. In a thermodynamic analysis we prove that the non-zero Tolman length is related to the adsorption of solvent at the interface. Similar, but not the same, correlations between the solvent adsorption and the Tolman length are found in the two scenarios. This result indicates that one should be careful with symmetry arguments in a Helfrich analysis, in particular for systems that have a finite interfacial tension: one not only should consider the structural symmetry of the interface, but also consider the constraints that are enforced upon imposing the curvature. The volume fraction of solvent, the chain length N as well as the interaction parameter chi(AB) in the system can be used to take the system in the direction of the critical point. The usual critical behavior is found. Both the width of the interface and the Tolman length diverge, whereas the density difference between the two phases, adsorbed amount of solvent at the interface, interfacial tension, spontaneous curvature, mean bending modulus as well as the Gaussian bending modulus vanish upon approach of the critical point.     

Noninteracting versus interacting poly(N-isopropylacrylamide)-surfactant mixtures at the air-water interface

Two polymer-surfactant mixtures have been studied at the air-water interface using neutron reflectivity and surface tension techniques. For the noninteracting system poly(N-isopropylacrylamide) (PNIPAM)/octaethyleneglycol mono n-decyl ether (C10E8), the adsorption behavior is competitive and driven purely by surface pressure (pi). When pi(polymer) > pi(surfactant), the surface layer consists of almost pure polymer, and for pi(polymer) < pi(surfactant), the polymer is displaced from the surface by the increasing pressure of the surfactant. Beyond the CMC, the polymer is completely displaced from the surface. For the interacting system PNIPAM/sodium dodecyl sulfate (SDS) where the two species interact strongly in the bulk beyond the critical aggregation concentration (CAC), the surface behavior is more original. Earlier neutron reflectivity studies investigated PNIPAM adsorption behavior where the SDS was contrast-matched to the solvent. In the present study, complementary measurements of SDS adsorption where PNIPAM is contrast-matched to the solvent give a complete view of the surface composition of the mixed system. At a constant polymer concentration, with increasing SDS, three main regimes are obtained. For C(SDS) < CAC, adsorption is governed by simple competition and PNIPAM is predominant at the interface. At intermediate SDS concentration (CAC < C(SDS) < x2, where x2 indicates the predominance of free SDS micelles), interfacial behavior is governed by bulk polymer-surfactant interaction. Adsorbed polymer is displaced from the interface to form PNIPAM-SDS complex in the bulk. SDS adsorption remains weak since most of the SDS molecules are used to form bulk polymer-surfactant aggregates. Further increase in SDS concentration results in continued displacement of PNIPAM and an abrupt increase in SDS adsorption. This is a result of saturation of bulk polymer chain with adsorbed micelles. Interestingly, beyond x2, PNIPAM is not completely displaced from the surface. A mixed PNIPAM-SDS adsorbed layer with enhanced packing of the SDS monolayer is formed.     

DNA separation at a liquid-solid interface

We demonstrate that it is possible to separate a broad band of DNA on a solid substrate without topological obstacles. The mobility was found to scale with molecular size (N) as N(-0.25), while the resolution scaled as N(0.75) indicating that diffusivity on this substrate was minimal. By varying the buffer concentration we were able to show that the mobility for a given chain length scaled with the persistent length (p) as p(1/2). This could be shown to be related to the Gaussian conformation of the chains adsorbed on the surface. A two-dimensional corrugated surface of nonporous silica beads was produced using a self-assembling process at the air/water interface. Even though the surface corrugations were comparable to persistence length we show that they do not affect the mobility, indicating that surface friction rather than topological constraints are the predominant mechanism of separation on a surface.     

Surface rheology of PEO-PPO-PEO triblock copolymers at the air-water interface: comparison of spread and adsorbed layers

The dilatational rheological properties of monolayers of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide)-type block copolymers at the air-water interface have been investigated by employing an oscillating ring trough method. The properties of adsorbed monolayers were compared to spread layers over a range of surface concentrations. The studied polymers were PEO26-PPO39-PEO26 (P85), PEO103-PPO40-PEO103 (F88), and PEO99-PPO65-PEO99 (F127). Thus, two of the polymers have similar PPO block size and two of them have similar PEO block size, which allows us to draw conclusions about the relationship between molecular structure and surface dilatational rheology. The dilatational properties of adsorbed monolayers were investigated as a function of time and bulk solution concentration. The time dependence was found to be rather complex, reflecting structural changes in the layer. When the dilatational modulus measured at different concentrations was replotted as a function of surface pressure, one unique master curve was obtained for each polymer. It was found that the dilatational behavior of spread (Langmuir) and adsorbed (Gibbs) monolayers of the same polymer is close to identical up to surface concentrations of approximately 0.7 mg/m2. At higher coverage, the properties are qualitatively alike with respect to dilatational modulus, although some differences are noticeable. Relaxation processes take place mainly within the interfacial layers by a redistribution of polymer segments. Several conformational transitions were shown to occur as the area per molecule decreased. PEO desorbs significantly from the interface at segmental areas below 20 A(2), while at higher surface coverage, we propose that segments of PPO are forced to leave the interface to form a mixed sublayer in the aqueous region.     

Applicability of polymer theories to the thermodynamics of proteins at the air/water interface: example of β-lactoglobulin

Knowledge of the equation of state of adsorbed or deposited layers of proteins at the air/water interface is of fundamental interest in the understanding of the surface activity of these molecules. Using scaling laws of current polymer theories, it has been shown that the equation of state of the interfacial layer in the semi-dilute regime should relate the surface pressure to the surface concentration through a power law. The exponent of this power law should reflect the quality of the solvent and the conformation of the adsorbed polypeptide chain. In the case of β-lactoglobulin layers, in the range of surface concentrations that should correspond to the semi-dilute regime, the relationship between surface pressure and surface concentration is expressed as a power law. The exponent of this power law is strongly influenced by the nature of the aqueous substrate and by the net charge of the protein molecule. The use of scaling laws gives a coherent view of the expansion of the polypeptide chain in the interfacial layer and of the relationship between surface concentration and surface pressure in the semi-dilute regime. This result favours a strong similarity between β-lactoglobulin and a polymer chain in the interfacial layer. It is concluded that current theories of polymer adsorption could be applied to interfacial protein layers.     

Apparent glassy dynamics of an adsorbed polymer chain in the bond-fluctuation model

The dynamics of a single homopolymer chain strongly adsorbed on a flat surface is investigated by Monte Carlo simulation using the bond-fluctuation model. Previously observed anomalous glassy dynamics at low temperatures [Phys. Rev. E 49 , 5420 (1994)] is revisited in detail. We also study the dynamics of a polymer chain confined in a narrow slit of width of a monomer and a modified bond-fluctuation model in three dimensions to include more relevant bond vectors. We show that the previously observed glassy dynamics is due to an artifact of the bond-fluctuation model in three dimensions in that it does not cross-over to the two dimensional bond-fluctuation model with the correct Rouse dynamics. With the proper inclusion of the extra bond vectors P(2,2,0) and P(3,2,0), no glassy behavior appears for the strongly adsorbed chain.     

Confinement of polystyrene at interfaces: Consequences on chain orientation

The knowledge of the structure and orientation of polymer chains adsorbed at an interface could be of major importance to predict the level of interfacial interactions and adhesion that depend strongly on the properties of the interface formed between the two materials (polymer and substrate) brought into contact. In this work, we were interested to study thin films of atactic polystyrene after adsorption (spin‐coating) on two chemically different substrates (inert and OH‐grafted gold substrates). The main aim is to analyze the resulting anisotropy due to the confinement in a quasi‐bidimensional geometry, as well as to investigate the incidence of the interfacial interactions, potentially established between the polymer and the surface, on the chain organization. Our infrared spectroscopy results allowed us to access the adsorption model of polystyrene chains and to highlight the relation between chain orientation and interfacial acid–base interactions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1268–1276, 2006     

Shape of Micelles Formed From Strongly Adsorbed Grafted Polymers in Poor Solvents

Summary: We consider the shape of strongly adsorbed polymer chains in poor solvents. Using both SCF theory and Monte Carlo simulations, we find these chains undergo an instability which is driven, surprisingly, by polymer entropy. This instability occurs above some critical grafting separation and the intermediate segregation regime. An analytical calculation also suggests that this instability occurs for strongly adsorbed polymer chains. We proceed to study multi‐chain systems and observe a number of novel morphological structures including circular polymer droplets, lamellae and a polymer layer with a solvent‐filled hole.

Shape of strongly adsorbed multi‐chain polymer globules.     

The adsorption of a copolymer of vinyl pyrrolidone and allylamine at the silica-solution interface

The conformation of a copolymer of vinyl pyrrolidone and allylamine adsorbed at the silica-solution interface has been studied by EPR spectroscopy. Spin labels attached at random along the polymer backbone have allowed the fractions of segments in trains and loops to be measured. The polymer changed from a relatively flattened conformation to a more looped one with increasing surface coverage; the effect on the conformation of changing solvent from pure water to 0–1 N NaCl or chloroform was small. The time for changes between the flattened and looped conformation was less than 2 min and bridging of the polymer molecules between silica particles was demonstrated.     

H/D isotopic exchange in water interactions with the ferroelectric copolymer: Poly(vinylidene fluoride-trifluoroethylene) (70%:30%)

For both water and heavy water adsorption and absorption on crystalline poly(vinylidene fluoride with trifluoroethylene (30%)), P(VDF-TrFE 70:30), two distinctly different adsorption sites have been identified by thermal desorption spectroscopy. One adsorbed water species resembles ice and there is also an absorbed water species that interacts more strongly with the polymer thin film, and in addition, there is a polymer surface (polymer to ice interface) water species. We find that there is H/D exchange between the water or heavy water molecules and the ferroelectric polymer (largely -(CH2-CF2)-), particularly at the polymer surface.     

Nonequilibrium simulations of filled polymer networks: searching for the origins of reinforcement and nonlinearity

We present nonequilibrium dissipative particle dynamics (DPD) simulations of cross-linked elastomers containing solid filler particles at 30% volume fraction. We study systematically the effect of the morphology (dispersed or aggregated particles) and of the effective particle-particle interactions. In addition, we have experimented by replacing the standard harmonic DPD bonds with other potential functions, conceived to deal with the finite extensibility of the polymer chains and the possibility of a slow equilibrium between strongly and weakly adsorbed chains at the rubber-filler interface. The simulation results shed some light on the basic mechanisms of rubber reinforcement, including the nonlinearity and history dependence commonly known as "Payne effect" and "Mullins effect."     

Unmixing of polymer blends confined in ultrathin films: crossover between two-dimensional and three-dimensional behavior

The interplay between chain conformations and phase separation in binary symmetric polymer mixtures confined into thin films by "neutral" hard walls (i.e., walls that do not preferentially attract or repel one of the two components of the mixture) is studied by Monte Carlo simulations. Using the bond fluctuation model on a simple cubic lattice in the semi grand canonical ensemble, we locate the critical temperature of demixing via finite size scaling methods for a wide range of chain lengths (16 infinity, and hence T(c) proportional, variant N. However, strong deviations from the Flory-Huggins theory occur as long as the unperturbed chain dimension exceeds D, and the critical behavior falls in the universality class of the two-dimensional Ising model for any finite value of D.