Effect of solvent quality on the conformations of a model comb polymer

The effect of solvent quality on the equilibrium structure of a densely branched comb polymer is investigated based on the structure factor analyses by off-lattice Monte Carlo simulations. First, theta temperature (theta(infinity)) must be determined to identify the solvent condition. We locate the characteristic temperature theta(A)(N) at which the second virial coefficient vanishes and the transition temperature theta(R)(N) at which radius of gyration R(g) of the chain varies most rapidly with temperature, i.e., d(2)R(g)/dT(2)|(theta(R)) = 0. N represents the total number of monomers of a comb. As N --> infinity, theta(A) and theta(R) coincide to a point that is identified as the true theta temperature (theta(infinity)). The structure factors of the main chain, the side chain, and the whole polymer are calculated, respectively. It is found that at T = theta(infinity), the structural factors S(qR(g)) for the overall comb polymers match quite well with those of their Gaussian counterparts. When T< theta(infinity), the overall comb polymer assumes collapsed conformations, similar to a homogeneous sphere. However, the structure factor of the side chain indicates that it always remains in an expanded state regardless of the solvent condition. It is attributed to the strong interactions between side chains. The same effect leads to enhanced rigidity of the main chain in comparison to the linear chain, as clearly observed from the rescaled Kratky plot.     

Higher virial coefficients of four and five dimensional hard hyperspheres

The seventh and eighth virial coefficients for hard hyperspheres are calculated by Monte Carlo techniques. It is found that B(7)/B(2) (6)=0.001 43+/-0.000 13 and 0.000 44+/-0.000 12 in four and five dimensions, respectively, and that B(8)/B(2) (7)=0.000 414+/-0.000 20 in four dimensions. These values are used to investigate various proposed equations of state. Comparisons against the molecular dynamics calculations of Luban and Michels show that their proposed semiempirical form is excellent at higher densities. Moreover, we confirm Santos observation in five dimensions that a suitable linear combination of the Percus-Yevick compressibility and virial equations of state fits the molecular dynamics data nearly as well as any other proposed form.     

Second virial coefficients of Lennard–Jones chains

The second virial coefficients B₂ of Lennard–Jones chain fluids were calculated through Monte Carlo integration as a function of chain length m (up to 48 segments) and temperature. We found that at a fixed temperature the second virial coefficient decreases with chain length. At low temperatures, the virial coefficient changes sign from positive to negative as m increases. The simulation data also provide an estimate for the theta temperature T_Θ at which the attractive and repulsive interactions cancel each other for dilute solutions. It is found that the theta temperature T_Θ for Lennard–Jones chains with m>32 is 4.65 independent of chain length m. A comparison of simulated values of B₂ with those evaluated from two different perturbation theories for chain fluid shows that these approximate theories underestimate the second virial coefficients of Lennard–Jones chains.     

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.     

弹性竿模型下超螺旋DNA分子的构象研究

采用弹性竿模型 (Elasticrodmodel) ,用MonteCarlo方法对DNA分子的构象进行研究 .通过计算发现 ,DNA分子的能量是由弯曲势能EB 和扭转势能ET 两部分组成 ,通常EB 比ET 大一至两个数量级 .同时给出了均方回转半径与链长之间的关系为〈R2g〉 =1 1 69 5 -3 5×n +0 0 2 5×n2 ,它体现了DNA分子结构的特点 .验证了公式Lk=Wr+Tw ,得出Lk与Wr比较接近的结论 ,考虑DNA分子的构型 ,意味着DNA分子容易被弯曲而不易被扭转 ,但随着连接系数的增加 ,DNA被扭转的几率也在增加 .这为分析DNA分子的结构特征提供了一种新方法     

Surface phase transitions in one-dimensional channels arranged in a triangular cross-sectional structure: theory and Monte Carlo simulations

Monte Carlo simulations and finite-size scaling analysis have been carried out to study the critical behavior in a submonolayer lattice-gas of interacting monomers adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure. Two kinds of lateral interaction energies have been considered: (1) w(L), interaction energy between nearest-neighbor particles adsorbed along a single channel and (2) w(T), interaction energy between particles adsorbed across nearest-neighbor channels. We focus on the case of repulsive transverse interactions (w(T)>0), where a rich variety of structural orderings are observed in the adlayer, depending on the value of the parameters k(B)Tw(T) (being k(B) the Boltzmann constant) and w(L)w(T). For w(L)w(T)=0, successive planes are uncorrelated, the system is equivalent to the triangular lattice, and the well-known ([square root] 3 x [square root] 3) [([square root] 3 x ([square root] 3)(*)] ordered phase is found at low temperatures and a coverage, theta, of 13. In the more general case (w(L)/w(T) not equal 0), a competition between interactions along a single channel and a transverse coupling between sites in neighboring channels leads to a three-dimensional adsorbed layer. Consequently, the ([square root] 3 x ([square root] 3) and (([square root] 3 x ([square root] 3)(*) structures "propagate" along the channels and new ordered phases appear in the adlayer. Each ordered phase is separated from the disordered state by a continuous order-disorder phase transition occurring at a critical temperature, T(c), which presents an interesting dependence with w(L)/w(T). The Monte Carlo technique was combined with the recently reported free energy minimization criterion approach (FEMCA) [F. Roma et al., Phys. Rev. B 68, 205407 (2003)] to predict the critical temperatures of the order-disorder transformation. The excellent qualitative agreement between simulated data and FEMCA results allows us to interpret the physical meaning of the mechanisms underlying the observed transitions.     

Computer simulation of linkage of two ring chains

We performed off-lattice Monte Carlo simulations of links of two model ring chains with chain length N up to 32,768 in the theta solution or amorphous bulk state by using a random walk model (Model I), and molecular dynamics simulations of two model ring chains in solution with excluded volume interaction (Model II) to investigate topological effects on the geometry of link and ring conformation. In the case of Model I, the mean squared linking number, its distribution, and the size of two chains with fixed linking number are investigated. Our simulation results confirm the previous theoretical prediction that the mean squared linking number decays as pe(-qs(2)) with the distance of centers of chain mass s, where p and q are found to be chain length dependent and q asymptotically approaches to 0.75 as chain length increases. The linking number distribution of two chains has a universal form for long chains, but our simulation results clearly show that the distribution function deviates from the Gaussian distribution, a fact not predicted by any previous theoretical work. A scaling prediction is proposed to predict the link size, and is checked for our simulations for the Model II. The simulation results confirmed the scaling prediction of the blob picture that the link with linking number m occupies a compact volume of m blobs, and the size of the link is asymptotic to R(L) ≈ bN(ν)m(1/3-ν), where N is the chain length, and v is the Flory exponent of polymer in solutions.     

Up to fourth virial coefficients from simple and efficient internal-coordinate sampling: application to neon

A simple and efficient internal-coordinate importance sampling protocol for the Monte Carlo computation of (up to fourth-order) virial coefficients ?B(n) of atomic systems is proposed. The key feature is a multivariate sampling distribution that mimics the product structure of the dominating pairwise-additive parts of the ?B(n). This scheme is shown to be competitive over routine numerical methods and, as a proof of principle, applied to neon: The second, third, and fourth virial coefficients of neon as well as equation-of-state data are computed from ab initio two- and three-body potentials; four-body contributions are found to be insignificant. Kirkwood-Wigner quantum corrections to first order are found to be crucial to the observed agreement with recent ab initio and experimental reference data sets but are likely inadequate at very low temperatures.     

Two-parameter model predictions and theta-point crossover for linear-polymer solutions

We consider the first few virial coefficients of the osmotic pressure, the radius of gyration, the hydrodynamic radius, and the end-to-end distance for a monodisperse polymer solution. We determine the corresponding two-parameter model functions which parametrize the crossover between the good-solvent and the ideal-chain behavior. These results allow us to predict the osmotic pressure and the polymer size in the dilute regime in a large temperature region above the theta point.     

Osmotic pressure and polymer size in semidilute polymer solutions under good-solvent conditions

We consider the lattice Domb-Joyce model at a value of the coupling for which scaling corrections approximately vanish and determine the universal scaling functions associated with the osmotic pressure and the polymer size for semidilute polymer solutions (c/c( *)相似文献   

Monte carlo calculations of second virial coefficients of chain molecules

Monte Carlo calculations have been performed for different types of chain molecules whose units interact through Lennard-Jones potentials. From the averaged Mayer function, we have evaluated the intermolecular two-body cluster integral, obtaining results for second virial coefficients. We have investigated the following points: a) the site modelization of alkanes by comparison of our results with gas phase data of different linear and branched alkanes and their mixtures. b) the prediction of interpenetration factors for flexible linear and star polymer chains in a good solvent (or excluded volume conditions). c) the determination of the theta point for a model of flexible polymer chains and the comparison of data for finite chains with theoretical predictions.     

Polymer translocation through a nanopore: a two-dimensional Monte Carlo study

We investigate the problem of polymer translocation through a nanopore in the absence of an external driving force. To this end, we use the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. To overcome the entropic barrier without artificial restrictions, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau required for the polymer to completely exit the pore on either end. We find numerically that tau scales with the chain length N as tau approximately N(1+2nu), where nu is the Flory exponent. This is the same scaling as predicted for the translocation time of a polymer which passes through the nanopore in one direction only. We examine the interplay between the pore length L and the radius of gyration R(g). For LR(g), we find tau approximately N. In addition, we numerically find the scaling function describing crossover between short and long pores. We also show that tau has a minimum as a function of L for longer chains when the radius of gyration along the pore direction R( parallel) approximately L. Finally, we demonstrate that the stiffness of the polymer does not change the scaling behavior of translocation dynamics for single-segment dynamics.     

Connection between the virial equation of state and physical clusters in a low density vapor

We carry out Monte Carlo simulations of physical Lennard-Jones and water clusters and show that the number of physical clusters in vapor is directly related to the virial equation of state. This relation holds at temperatures clearly below the critical temperatures, in other words, as long as the cluster-cluster interactions can be neglected--a typical assumption used in theories of nucleation. Above a certain threshold cluster size depending on temperature and interaction potential, the change in cluster work of formation can be calculated analytically with the recently proposed scaling law. The breakdown of the scaling law below the threshold sizes is accurately modeled with the low order virial coefficients. Our results indicate that high order virial coefficients can be analytically calculated from the lower order coefficients when the scaling law for cluster work of formation is valid. The scaling law also allows the calculation of the surface tension and equilibrium vapor density with computationally efficient simulations of physical clusters. Our calculated values are in good agreement with those obtained with other methods. We also present our results for the curvature dependent surface tension of water clusters.     

A general simulation method for computing conformational properties of single polymer chains

Rotational isomeric state (RIS) theory is the standard method for computing the conformational statistics of polymer chains. It applies to chains under theta conditions, either in the melt or in theta solution. RIS statistical weights can also be used in a Monte Carlo scheme for generating independent chain conformations with the correct statistics. One practical drawback of RIS methods is that statistical weights must be derived before any chain properties can be calculated. This can be tedious for all but relatively simple chains. Here, an efficient method is presented for computing the properties of theta chains without the intermediate step of deriving statistical weights. The method—‘RIS’ Metropolis Monte Carlo (RMMC) simulation-allows computation of the same type of properties as does RIS theory. It shares certain approximations with RIS theory but is not, strictly speaking, a rotational isomeric state method, as it allows bond torsion angles to vary continuously.     

The scaling behavior of the second virial coefficient of linear and ring polymer

The scaling behavior of the second virial coefficient of ring polymers at the theta temperature of the corresponding linear polymer(θ_L) is investigated by off-lattice Monte Carlo simulations. The effects of the solvents are modeled by pairwise interaction between polymer monomers in this approach. Using the umbrella sampling, we calculate the effective potential U(r) between two ring polymers as well as the second virial coefficient A_2 of ring polymers at θ_L, which results from a combination of 3-body interactions and topological constraints. The trend in the strength of the effective potential with respect to chain length shows a non-monotonic behavior, differently from that caused only by topological constraints. Our simulation suggests that there are three regimes about the scaling behavior of A_2 of ring polymers at θ_L: 3-body interactions dominating regime, the crossover regime, and the topological constraints dominating regime.     

Simulations of concentrated suspensions of rigid fibers: relationship between short-time diffusivities and the long-time rotational diffusion

Brownian dynamics simulations of the behavior of suspensions of fibers demonstrate that the scaling of the rotational diffusivity with respect to the number density (nL3) is a sensitive function of the thickness and the parameter L2D(R0)/D(T0), where D(R0) is the rotational diffusivity at infinite dilution, D(T0) is the average center-of-mass diffusivity at infinite dilution, and L is the fiber length. Existing theories for the long-time rotational diffusivities of rigid fibers in the semidilute and concentrated regimes fail to accurately account for the relationship with the dilute values of the rotational and translational diffusivities of the various physical models used to simulate the fibers. The concentration regime studied in this work ranges from a number density of nL3 approximately 0-150, which is below the transition from an isotropic to nematic state. The effect of the fiber thickness was studied by performing simulations of rods with aspect ratios (fiber length over diameter) of 25, 50, and 500, as well as performing projections for infinitely thin fibers. The excluded volume of the rods was enforced through the use of short-range potentials. For a rod with an aspect ratio of 50 with a parameter of L2D(R0)/D(T0)=9, which corresponds to a slender-body model of the individual fibers, the rotational diffusivity (D(R)) scales as D(R)/D(R0) approximately (nL3)(-1.9) in the concentration regime of 70 < or = nL3 < or = 150. Similarly with a parameter of L2D(R0)/D(T0)=4, corresponding to a rigid-dumbbell model, the rotational diffusivity scales as D(R)/D(R0) approximately (nL3)(-1.1) over the same range of concentrations. For rods with aspect ratios of 25, it is observed that a difference in the scaling is seen for L2D(R0)/D(T0) approximately < 8, with higher values of this ratio exhibiting essentially the same scaling. Additional values of the ratio L2D(R0)/D(T0) were investigated to determine the overall behavior of the suspension dynamics with respect to this parameter. These findings resolve discrepancies between simulation results for rotational diffusivities reported by previous investigators and provide new insights for the development of an accurate theory for the diffusivity of rigid rods suspended in solution.     

Structure, dynamics, and phase transitions of tethered membranes: a Monte Carlo simulation study

A coarse-grained model of a self-avoiding tethered membrane with hexagonal coordination, embedded in three-dimensional space, is studied by means of extensive Monte Carlo computer simulations. The simulations are performed at various temperatures for membranes with linear size 5< or =L< or =50. We find that the membrane undergoes several folding transitions from a high-temperature flat phase to multiple-folded structure as the temperature is steadily decreased. Using a suitable order parameter and finite size scaling analysis, these phase transitions are shown to be of first order. The equilibrium shape of the membranes is analyzed by calculating the eigenvalues lambda(max) (2)> or =lambda(med) (2)> or =lambda(min) (2) of the inertia tensor. We present a systematic finite size scaling analysis of the radius of gyration and the eigenvalues of the inertia tensor at different phases of the observed folding transitions. In the high-temperature flat phase, the radius of gyration R(g) grows with the linear size of the membrane L as R(g) proportional to L(nu), where the exponent nu is approximately equal to 1.0. The eigenvalues of the inertia tensor scale as lambda(max) proportional to lambda(med) proportional to L(nu) and lambda(min) proportional to L(nu(min) ), whereby the roughness exponent nu(min) is approximately equal to 0.7. We also find that the time tau(R) of a self-avoiding membrane to diffuse a distance R(g) scales as tau(R) proportional to L(2nu+2), which is in good agreement with the theoretical predictions.     

How does solvent molecular size affect the microscopic structure in polymer solutions?

Monte Carlo simulation has been used to investigate the effects of linear solvent molecular size on polymer chain conformation in solutions. Increasing the solvent molecular size leads to shrinkage of the polymer chains and increase of the critical overlap concentrations. The root-mean-square radius of gyration of polymer chains (R(g)) is less sensitive to the variation of polymer concentration in solutions of larger solvent molecules. In addition, the dependency of R(g) on polymer concentration under normal solvent conditions and solvent molecular size is in good agreement with scaling laws. When the solvent molecular size approaches the ideal end-to-end distance of the polymer chain, an extra aggregation of polymer chains occurs, and the solvent becomes the so-called medium-sized solvent. When the size of solvent molecules is smaller than the medium size, the polymer chains are swollen or partially swollen. However, when the size of solvent molecules is larger than the medium size, the polymer coils shrink and segregate, enwrapped by the large solvent molecules.     

Surface order-disorder phase transitions and percolation

In the present paper, the connection between surface order-disorder phase transitions and the percolating properties of the adsorbed phase has been studied. For this purpose, four lattice-gas models in the presence of repulsive interactions have been considered. Namely, monomers on honeycomb, square, and triangular lattices, and dimers (particles occupying two adjacent adsorption sites) on square substrates. By using Monte Carlo simulation and finite-size scaling analysis, we obtain the percolation threshold theta(c) of the adlayer, which presents an interesting dependence with w/k(B)T (w, k(B), and T being the lateral interaction energy, the Boltzmann constant, and the temperature, respectively). For each geometry and adsorbate size, a phase diagram separating a percolating and a nonpercolating region is determined.     

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.