Phase behavior of semiflexible polymer chains

Monte Carlo simulations were performed on semiflexible polymer chains with the goal of delineating their isotropic-nematic (IN) and gas-liquid coexistence envelopes. The chain monomers are spherical beads that interact via a square-well potential with all other beads. Bonded beads are connected by strings chosen so that bond length varies between 1.01sigma and 1.05sigma (where sigma is the hard sphere diameter). The stiffness of the molecules is controlled via a potential between beads separated by two bonds; this potential restricts the distance between these beads to be between 2.02sigma and 2.1sigma. The vapor-liquid coexistence and IN coexistence curves are obtained using computer simulations. An IN transition is found for 10相似文献   

Molecular alignment of rigid rods in nonrigid spherical pores

We have investigated the orientation ordering of two shish-kebab chains confined by spherically harmonic potentials through Monte Carlo simulations and asymptotic analysis. The rigid rod is modeled as shish-kebab chains consisting of tangent hard spheres aligned in the same axis, and the harmonic potential is chosen to model nonrigid cavities. We first show that the interactions between a rod and the spherically harmonic potential are independent of chain orientation, indicating that the alignment of two confined rods arises from the excluded volume interactions alone. In the strong fields, the order parameter of two confined rods converges to different values, depending on the parity of chain length. From asymptotic order parameters, we find that the rods of odd-number beads rotate more freely even under the limiting strong confinement. However, the two rods of even-number beads are essentially trapped in a configuration of perpendicular alignment through intercalation of their central grooves. We attribute the dependence of the parity of chain length to the different locations of the center-of-mass in a rod for these two cases. Furthermore, we compare the shish-kebab chains with different rod models in the simulations, and utilize these models to explore the effect of the local rod smoothness on molecular alignment. Our findings suggest that increasing local rod smoothness enhances the rotational degree of freedom for confined rods, and the effect of local rod roughness emerges under strong enough applied potentials.     

Electrophoresis of Spherical Particles with a Random Distribution of Zeta Potential or Surface Charge

Electrophoresis is often used to measure the "average" zeta (zeta) potential on particles. However, it has been found by previous researchers that in making predictions of colloidal forces and stability, the distribution of zeta potential on the particles is important. This paper provides a straightforward method for measuring charge nonuniformity on colloidal spheres. It is shown that if the charge or zeta potential is random on a group of spheres, each covered with N equal-area patches, then the average magnitude of the dipole moment on the spheres is 0.92sigma(zeta)/N, and the average magnitude of the quadrupole moment is 1.302sigma(zeta)/N, where sigma(zeta) is the standard deviation of zeta potential over the surface of individual spheres. This is true for any random distribution of zeta potential, and the results emphasize that "random" implies nonuniform. It is demonstrated that since typical translational mobility measurements are much less sensitive to random charge nonuniformity than rotational mobility measurements, the latter measurement is better suited for measuring the second moment (sigma(zeta)) of zeta potential. Monte Carlo simulations were done to confirm and extend the analytical results. Copyright 2000 Academic Press.     

The Local and Collective Mobility in Polymer Chains and Networks with Included Rigid Particles Elastically Connected with the Network

Summary: The theory of molecular mobility of a polymer network with included rod-like particles is developed. The case is considered when the length of rods is comparable or greater than the average distance between neighboring cross-links of the primary network. The long-scale dynamics of the network is described by means of a regular cubic “coarse-grained” model. The junctions of this model describe the great network fragments (domains) the sizes of which are near to the average distance between neighboring rods.The quasi-elastic interactions between rods and network fragments lead to a broad relaxation spectrum for included rods as compared with free rods which are characterized by a single relaxation time of rotational diffusion. The frequency dependence of the dielectric loss factor of included rods is calculated for rods with permanent dipole moments directed parallel to the long axes of the rods chaotically distributed in the network. The frequency dependence of dynamic modulus of a polymer network with included rods is obtained. The increment in the dynamic modulus of the relatively short network motions (smaller than the distance between rods) also is taken into account. The broad relaxation spectrum of included rods leads to appearance of several maximums on the frequency dependences of both the dielectric loss factor and dynamical modulus.     

Influence of the reaction mechanism on the time course of the entropy production during reversible polymerization

The paper shows the influence of the reaction mechanism on the time course of the entropy production sigma in a closed system during reversible polymerization. We consider two different reaction mechanisms with (a) being a polycondensation and (b) a chain growth mechanism. For both mechanisms explicit expressions for the entropy production sigma as a function of time t are derived. To demonstrate the application of these general expressions we consider two different polymerization experiments where the reaction starts (i) from monomer molecules polymerizing to a defined number average chain length x(n,eq) and (ii) from monodisperse polymer molecules reacting with each other under the constraint that x(n) is the same at the beginning and the end of the reaction. In both cases we treat the system to be ideal and describe the kinetics of the reversible polymerization reactions using two kinetic constants for the forward and backward reactions, respectively. Under these assumptions the difference in the curvature of the entropy production sigma between a polycondensation and a chain growth mechanism is only marginal if the reaction starts from monomer molecules polymerizing to a defined number average chain length x(n,eq).     

Nanoscale colloids in a freely adsorbing polymer solution: a Monte Carlo simulation study

A key issue in nanoscale materials and chemical processing is the need for thermodynamic and kinetic models covering colloid-polymer systems over the mesoscopic length scale (approximately 1-100 nm). We have applied Monte Carlo simulations to attractive nanoscale colloid-polymer mixtures toward developing a molecular basis for models of these complex systems. The expanded ensemble Monte Carlo simulation method is applied to calculate colloid chemical potentials (micro(c)) and polymer adsorption (gamma) in the presence of freely adsorbing Lennard-Jones (LJ) homopolymers (surface modifiers). gamma and micro(c) are studied as a function of nanoparticle diameter (sigma(c)), modifier chain length (n) and concentration, and colloid-polymer attractive strength over 0.3 < Rg/sigma(c) < 6 (Rg is the polymer radius of gyration). In the attractive regime, nanocolloid chemical potential decreases and adsorbed amount increases as sigma(c), or n is increased. The scaling of gamma with n from the simulations agrees with the theory of Aubouy and Raphael (Macromolecules 1998, 31, 4357) in the extreme limits of Rg/sigma(c). When Rg/sigma(c) is large, the "colloid" approaches a molecular size and interacts only locally with a few polymer segments and gamma approximately n. When Rg/sigma(c) is small, the system approaches the conventional colloid-polymer size regime where multiple chains interact with a single particle, and gamma approximately sigma(c)2, independent of n. In contrast, adsorption in the mesoscopic range of Rg/sigma(c) investigated here is represented well by a power law gamma approximately n(p), with 0 < p < 1 depending on concentration and LJ attractive strength. Likewise, the chemical potential from our results is fitted well with micro(c) approximately n(q)sigma(c)3, where the cubic term results from the sigma(c) dependence of particle surface area (approximately sigma(c)2) and LJ attractive magnitude (approximately sigma(c)). The q-exponent for micro(c) (micro(c) approximately n(q)) varies with composition and LJ attractive strength but is always very close to the power exponent for gamma (gamma approximately n(p)). This result leads to the conclusion that in attractive systems, polymer adsorption (and thus polymer-colloid attraction) dominates the micro(c) dependence on n, providing a molecular interpretation of the effect of adsorbed organic layers on nanoparticle stability and self-assembly.     

Yield Stress of Concentrated Zirconia Suspensions: Correlation with Particle Interactions

The presence of a sufficient concentration of solid particles in a solution gives rise to a large increase in its viscosity and, more importantly, to significant deviations with respect to its original Newtonian behavior. Different rheological techniques are available to characterize such deviations, but the simplest one, obtention of steady-state rheograms, is already extremely useful with that purpose. In this work, this technique is applied to suspensions of zirconia particles, both synthesized with spherical geometry and commercial. The sigma(shear stress)-gamma;(shear rate) curves show that the suspensions are nonideal plastic, thus exhibiting a finite yield stress, sigma(0), and a shear-thinning flow. It is through sigma(0) that a connection can be established between steady-state rheological behavior and interaction energy between particles, since sigma(0) can be estimated as the maximum attractive force between particles multiplied by the number of bonds per unit area between a given particle and its neighbors. Having an experimental determination of sigma(0), the verification of its relation with the attractive forces requires estimation of the potential energy of interaction between any pair of particles. Two approaches will be considered: one is the classical DLVO model, in which the potential energy, V, is the sum of the van der Waals (V(LW)) and electrostatic (V(EL)) contributions. The second approach is the so-called extended DLVO theory, in which the acid-base interaction V(AB) (related to the hydrophilic repulsion or hydrophobic attraction between the particles) is considered in addition to V(LW) and V(EL). The three contributions can be calculated as a function of the interparticle distance if the particle-solution interface is characterized from both the electric and the thermodynamic points of view. The former is carried out by means of electrophoretic mobility measurements and the latter by contact angle determinations for three probe liquids on zirconia powder layers. Comparison between measured and calculated sigma(0) values was carried out for suspensions of spherical, monodisperse ZrO(2) particles, with volume fraction of solids, straight phi, ranging between 4.6 and 21.7%, in 10(-3) M NaCl solutions. In the case of commercial particles, the effects of both NaCl concentration (10(-5) to 10(-1) M) and volume fraction (3.5 to 21%) were investigated. It is found that the classical DLVO theory cannot be used to predict the yield stress when [NaCl]=10(-5) M, since the high zeta potentials and thick double layers never yield partial differential V/ partial differential R>0 (the interaction is repulsive for all distances) in such a case. A similar problem was encountered in 10(-1) M solutions, but now because V is always attractive, and no maximum force can be found. On the contrary, the extended DLVO model always yield physically reasonable sigma(0) values (coincident with those deduced from the classical approach when calculation is possible in the latter case). The comparison with experimental data shows that theory clearly underestimates sigma(0) by one order of magnitude or even more. The possible role of particle aggregation in this underestimation is discussed in terms of the scaling behavior of sigma(0) as a function of straight phi. Copyright 2000 Academic Press.     

Streaming potential generated by a long viscous drop in a capillary

The streaming potential generated by motion of a long drop of viscosity mu(d) = lambdamu in a uniform circular capillary filled with fluid of viscosity mu is investigated by means of a model previously used to study electrophoresis of a charged mercury drop in water. The capillary wall is at potential zeta c relative to the bulk fluid within it, and the surface of the drop is at potential zeta(d). Potentials are assumed to be sufficiently small so that the charge cloud is described by the linearized Poisson-Boltzmann equation, and the Debye length characterizing the thickness of the charge cloud is assumed to be thin compared with the gap h(0) between the drop and the capillary wall. Ions in the external fluid are not allowed to discharge at the surface of the drop, and the wall of the capillary has a nonzero surface conductivity sigma c. The drop is assumed to be sufficiently long so that end effects can be neglected. Recirculation of fluid within the drop gives rise to an enhanced streaming current when zeta(d) is nonzero, leading to an anomalously high streaming potential. This vanishes as the drop viscosity becomes large. If V is the velocity of the drop and gamma is the coefficient of interfacial tension between the two fluids, then the capillary number is Ca = mu V/gamma, and the gap varies as h(0)planck'sCa(2/3). When Ca is small, the gap h(0) is small and electrical conduction along the narrow gap is dominated by the surface conductivity sigma(c) of the capillary wall, which is constant. The electrical current convected by flowing fluid is proportional to Ca, as is the change in streaming potential caused by the presence of the drop. If sigma(c) = 0, then the electrical conductance of the gap depends on its width h(0) and on the bulk fluid conductivity sigma and becomes small as h(0) approximately equal to Ca(2/3) --> 0. The streaming potential required to cancel the O(Ca) convection current therefore varies as Ca(1/3). If sigma(c) = 0 and the drop is rigid (lambda --> infinity), then the change in streaming potential over and above that expected due to the change in pressure gradient is proportional to the difference in potentials zeta(c)-zeta(d).     

Generalized anomeric interpretation of the "high-energy" N-P bond in N-methyl-N'-phosphorylguanidine: importance of reinforcing stereoelectronic effects in "high-energy" phosphoester bonds

Electronic structure calculations have been performed on a model N-phosphorylguanidine, or phosphagen, to understand the stereoelectronic factors contributing to the lability of the "high-energy" N-P bond. The lability of the N-P bond is central to the physiological role of phosphagens involving phosphoryl transfer reactions important in cellular energy buffering and metabolism. Eight protonated forms of N-methyl-N'-phosphorylguanidine have been energy minimized at levels of theory ranging up to B3LYP/6-311++G(d,p) and MP2/6-311++G(d,p) to investigate the correlation between protonation state and N-P bond length. Selected forms have also been minimized using the CCSD/6-311++G(d,p) and QCISD/6-311++G(d,p) levels of theory. Bulk solvation energies using the polarized continuum model (PCM) with B3LYP/6-311++G(d,p) test the influence of the surroundings on computed structures and energies. The N-P bond length depends on the overall protonation state where increased protonation at the phosphoryl group or deprotonation at the unsubstituted N' nitrogen results in shorter, stronger N-P bonds. Natural bond orbital analysis shows that the protonation state affects the N-P bond length by altering the magnitude of stabilizing n(O) --> sigma*(N-P) stereoelectronic interactions and to a lesser extent the sigma(N-P) --> sigma*(C-N') and sigma(N-P) --> sigma*(C-N) interactions. The computations do not provide evidence of a competition between the phosphoryl and guanidinium groups for the same lone pair on the bridging nitrogen, as previously suggested by opposing resonance theory. The computed n(O) --> sigma*(N-P) anomeric effect provides a novel explanation of "high-energy" N-P bond lability. This offers new mechanistic insight into phosphoryl transfer reactions involving both phosphagens and other biochemically important "high-energy" phosphoester bonds.     

Synthesis of monodisperse high-aspect-ratio colloidal silicon and silica rods

We describe the synthesis and the physical properties of suspensions of colloidal silicon and silica rodlike particles. In addition to pure silicon and pure silica rods, we have also synthesized silicon rods with a silica shell and silica rods with a fluorescent silica layer. Pre-patterned p-type (100) silicon wafers were electrochemically etched in electrolyte solutions containing hydrogen fluoride. By the current density being varied while etching, macropores were etched with controllable modulated pore diameters. These silicon structures were transformed into rods with indentations 5.5 mum apart and with lengths up to 100 mum using iterative oxidation in air and dissolution of the silica by HF. Complete oxidation of these rods was also achieved. Sonication of the modulated rods resulted in monodisperse particles of 5.5 mum length and 300 nm width. A high yield of 10(12) particles, or more, is possible with this method. At high concentrations, these particles show nematic ordering in charge-stabilized suspensions. The oxidized silica outer layer of the silicon rods makes the further growth of silica in solution or on a wafer possible. This allows for control of the particles' interaction potential. Labeling with a fluorescent dye and index matching of the complete silica rods enable the study of concentrated dispersions quantitatively, on a single particle level, with confocal microscopy. Because of their high refractive index in the near-IR, the nematic phases of rods with a silica core are also interesting for photonic applications.     

The effects of shape and flexibility on bio-engineered fd-virus suspensions

We present a theoretical model to describe binary mixtures of semi-flexible rods, applied here to fd-virus suspensions. We investigate the effects of rod stiffness on both monodisperse and binary systems, studying thick-thin and long-short mixtures. For monodisperse systems, we find that fd-virus particles have to be made extremely stiff to even approach the behavior of rigid rods. For thick-thin mixtures, we find increasingly rich phase behavior as the rods are either made more flexible or if their diameter ratio is increased. For long-short rod mixtures we find that the phase behavior is controlled by the relative stiffness of the rods, with increasing the stiffness of the long rods or decreasing that of the short rods resulting in richer phase behavior. We also calculate the state point dependent effective shape of the rods. The flexible rods studied here always behave as shorter, thicker rigid rods, but with an effective shape that varies widely throughout the phase diagrams, and plays a key role in determining phase behavior.     

Evaluation of an atomic force microscopy pull-off method for measuring molecular weight and polydispersity of polymer brushes: effect of grafting density

The accuracy of the molecular weights Mn and polydispersities of polymer brushes, determined by stretching the grafted chains using atomic force microscopy (AFM) and measuring the contour length distribution, was evaluated as a function of grafting density sigma. Poly(N,N-dimethylacrylamide) brushes were prepared by surface initiated atom transfer radical polymerization on latex particles with sigma ranging between 0.17 and 0.0059 chains/nm2 and constant Mn. The polymer, which could be cleaved from the grafting surface by hydrolysis and characterized by gel permeation chromatography (GPC), had a Mn of 30,600 and polydispersity (PDI) of 1.35. The Mn determined by the AFM technique for the higher density brushes agreed quite well with the GPC results but was significantly underestimated for the lower sigma. At high grafting density in good solvent, the extended structure of the brush increases the probability of forming segment-tip contacts located at the chain end. When the distance between chains approached twice the radius of gyration of the polymer, the transition from brush to mushroom structure presumably enabled the formation of a larger number of segment-tip contacts having separations smaller than the contour length, which explains the discrepancy between the two methods at low sigma. The PDI was typically higher than that obtained by GPC, suggesting that sampling of chains with above average contour length occurs at a frequency that is greater than their spatial distribution.     

The influence of the salt concentration on the aggregation behavior of viscoelastic detergents

The influence of excess NaCl on the properties of viscoelastic detergent solutions of Cetypyridiniumsalicylate (CPySal) has been studied by static and dynamic light scattering, electric birefringence and rheological measurements. It is obeserved that the rodlike micelles of length L which are present in these solutions and which are responsible for their elastic properties grow in length with the increase of the NaCl concentration. As long as the rods are shorter than their mean distance, their length can be determined from the rheological and electric birefringence measurements. For very small shear fields these solutions behave as Newtonian fluids. The viscosity of the solution increases strongly when the rods begin to overlap. Solutions with overlapping rods are elastic. It is postulated from the results that the cmc_II (the critical concentration above which rods are present) and the length L of the rods are partially determined by the intermicellar interaction energy. It is furthermore postulated that this intermicellar interaction energy has an influence on the polydispersity of the rods and seems to make the rods relatively monodisperse.     

Residue-specific 13C' CSA tensor principal components for ubiquitin: correlation between tensor components and hydrogen bonding

The residue-specific 13C' CSA tensor principal components, sigma(11), sigma(22), sigma(33), and the tensor orientation defined by the rotation angles beta and gamma have been determined by solution NMR for uniformly labeled ubiquitin partially aligned in four different media. Spurious chemical shift deviations due to solvent effects were corrected with an offset calculated by linear regression of the residual dipolar couplings and chemical shifts at increasing alignment strengths. Analysis of this effect revealed no obvious correlation to solvent exposure. Data obtained in solution from a protein offer a better sampling of 13C' CSA for different amino acid types in a complex heterogeneous environment, thereby allowing for the evaluation of structural variables that would be challenging to achieve by other methods. The 13C' CSA principal components cluster about the average values previously determined, and experimental correlations observed between sigma(11), sigma(22) tensorial components and C'O...H(N) hydrogen bonding are discussed. The inverse association of sigma(11) and sigma(22) exemplify the calculated and solid-state NMR observed effect on the tensor components by hydrogen bonding. We also show that 13C' CSA tensors are sensitive to hydrogen-bond length but not hydrogen-bond angle. This differentiation was previously unavailable. Similarly, hydrogen bonding to the conjugated NH of the same peptide plane has no detectable effect. Importantly, the observed weak correlations signify the presence of confounding influences such as nearest-neighbor effects, side-chain conformation, electrostatics, and other long-range factors to the 13C' CSA tensor. These analyses hold future potential for exploration provided that more accurate data from a larger number of proteins and alignments become available.     

Depletion potentials in colloidal mixtures of hard spheres and rods

The depletion potential between a hard sphere and a planar hard wall, or two hard spheres, imposed by suspended rigid spherocylindrical rods is computed by the acceptance ratio method through the application of Monte Carlo simulation. The accurate results and ideal-gas approximation results of the depletion potential are determined with the acceptance ratio method in our simulations. For comparison, the depletion potentials are also studied by using both the density functional theory and Derjaguin approximations. The density profile as a function of positions and orientations of rods, used in the density functional theory, is calculated by Monte Carlo simulation. The potential obtained by the acceptance ratio method is in good agreement with that of density functional theory under the ideal-gas approximation. The comparison between our results and those of other theories suggests that the acceptance ratio method is the only efficient method used to compute the depletion potential induced by nonspherical colloids with the volume fraction beyond the ideal-gas approximation.     

Topologically entangled polymers

Summary The statistical mechanics of a ring polymer confined to a plane and entangled with many randomly placed thin rods perpendicular to the plane are considered. The entanglements are characterized by the Gauss linking number. If the statistics of the random distribution of the rods is given by only the second cumulant then it is shown that the resulting entanglement problem can be solved formally exactly. For this special case the exact solution becomes possible because the problem can be reduced to one involving the winding of the polymer around one infinitely thin rod. The exact solution can be obtained for both the annealed and the quenched random distribution of obstacles. The entanglement of the ring polymer around the obstacles leads to a repulsive topological potential which is an effective interaction between the polymer and the rods. The origin of this potential is solely due to the constraint that the winding number be conserved. It is shown that forR ²/Lll (R is the location of the polymer segment,L is the total length of the polymer, andl is the length of the monomer) the topological potential for the annealed random case goes asN ln ln(Ll/R ²) whereN is the number of obstacles whereas for the quenched random case the potential is given byC lnLl/R ², whereC is a numerical constant that depends onN.     

The vanishing limit of the square-well fluid: the adhesive hard-sphere model as a reference system

We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical point B2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect if the critical temperature Tc is estimated via a constant B2*c assumption, due to the highly nonlinear transformation between B2*c and Tc. This explains the previously observed validity of the law of corresponding states. The critical density rho c is also found to be constant when measured in units of the cube of the average distance between two bonded particles (1+0.5 delta)sigma. The possibility of describing the delta-->0 dependence with precise functional forms provides improved accurate estimates of the critical parameters of the adhesive hard-sphere model.