高分子链形状与尺寸关联的Monte Carlo模拟

运用MonteCarlo方法对线型高分子链格点模型的构型进行了模拟,研究了构型的尺寸(采用平方末端距R²,平方回转半径S²来表征)和形状(由非球形因子A表征)之间的关联.对任何长度的高分子链,其关联系数CA,R²和CA,S²均为正值,表明高分子链的形状与尺寸之间存在正关联,即尺寸小的构型其非球形因子A一般也小,反之尺寸大的构型其非球形因子A一般也大.关联系数CA,R²和CA,S²均随链长的增大而减小,近似地与链长的倒数(n^-1)成正比.研究还表明,关联系数的极限值(链长n很大时)与格点的类型无关,与链样本产生的方式也无关,但与链是否考虑排斥体积有关,考虑了排斥体积后,关联系数增大.     

Study of the polymer interaction with a surface by entropic sampling

By means of a variant of the Monte Carlo method (entropic sampling within the Wang-Landau algorithm) the models of the interaction of a neutral polymer with a flat surface are studied. The method yields distribution functions over the energy and the distance from the polymer to the surface. Based on these distributions, excess entropies of the systems and their thermal properties are calculated: internal energy, heat capacity, average radius of gyration, average chain end-to-end distance, and average distance from the polymer to the surface. Continuous and lattice models are considered.     

Simulations on the reinforcement of poly(dimethylsiloxane) elastomers by randomly distributed filler particles

Monte Carlo computer simulations were carried out on filled networks of poly(dimethylsiloxane) (PDMS), which were modeled as composites of crosslinked chains and randomly arranged spherical filler particles. The primary concern of the investigation was the effect of the excluded volume of these particles on the elastomeric properties of the polymers. Calculations were carried out for PDMS chains with different molecular masses between crosslinks, and for filler particles with different sizes and at various volume percentages. Distributions of end-to-end vectors for both unfilled and filled networks were obtained using Monte Carlo simulations based on rotational isomeric state (RIS) theory. More extended configurations, with a higher end-to-end distance, were observed for networks filled with smaller particles. The nominal stress f* and the modulus or reduced nominal stress [f*] were calculated from the distributions of end-to-end vectors using the Mark-Curro approach. Relatively small filler particles were found to increase the non-Gaussian behavior and to increase the normalized moduli above the reference value of unity. Temperature effects on the stress were also investigated. © 1996 John Wiley & Sons, Inc.     

Excluded volume scaling for polymers

The excluded volume of several polymers in the dilute solution regime is calculated using the Monte Carlo integration. The calculated scaling exponent, λ, for the excluded volume for a polymer chain with another chain of the same length is 1.74±0.02. This exponent is consistent with the idea that the interaction of chains with one another in a good solvent is similiar to the interaction of two hard spheres. The effective radius of the hard sphere is proportional to the radius of gyration which has a scaling exponent of ν=0.595±0.005. This result is close to the theoretical value of 0.589. This study establishes the relationship λ=3ν.     

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.     

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   

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.     

Radial distribution function of freely jointed hard-sphere chains in the solid phase

Monte Carlo simulation is used to generate the radial distribution function of freely jointed tangent-bonded hard-sphere chains in the disordered solid phase for chain lengths of three, four, six, and eight segments. The data are used to create an accurate analytical expression of the total radial distribution function of the hard-sphere chains that covers a density range from the solidification point up to a packing fraction of 0.71. It is envisioned that the correlation will help further progress toward molecular thermodynamic treatment of the solid phase in general and toward perturbed chain theories for the solid phase, in particular.     

An analytical approximation for the orientation-dependent excluded volume of tangent hard sphere chains of arbitrary chain length and flexibility

Onsager-like theories are commonly used to describe the phase behavior of nematic (only orientationally ordered) liquid crystals. A key ingredient in such theories is the orientation-dependent excluded volume of two molecules. Although for hard convex molecular models this is generally known in analytical form, for more realistic molecular models that incorporate intramolecular flexibility, one has to rely on approximations or on computationally expensive Monte Carlo techniques. In this work, we provide a general correlation for the excluded volume of tangent hard-sphere chains of arbitrary chain length and flexibility. The flexibility is introduced by means of the rod-coil model. The resulting correlation is of simple analytical form and accurately covers a wide range of pure component excluded volume data obtained from Monte Carlo simulations of two-chain molecules. The extension to mixtures follows naturally by applying simple combining rules for the parameters involved. The results for mixtures are also in good agreement with data from Monte Carlo simulations. We have expressed the excluded volume as a second order power series in sin?(γ), where γ is the angle between the molecular axes. Such a representation is appealing since the solution of the Onsager Helmholtz energy functional usually involves an expansion of the excluded volume in Legendre coefficients. Both for pure components and mixtures, the correlation reduces to an exact expression in the limit of completely linear chains. The expression for mixtures, as derived in this work, is thereby an exact extension of the pure component result of Williamson and Jackson [Mol. Phys. 86, 819-836 (1995)].     

Evaluations of forcefields for aromatic polysiloxanes,and some applications to poly(diphenylsiloxane)

Two forcefields were evaluated for possible use in polysiloxanes containing aromatic phenyl or phenylene groups, either as side chains or as part of the chain backbone. The criterion was reproducing results on the crystal structure of the cyclic diphenylsiloxane trimer, and both forcefields were satisfactory. The better of the two was used to obtain conformational energies for estimating some of the statistical properties of the corresponding polymer poly(diphenylsiloxane) (PDPS) [Si(C₆H₅)₂–O–]. The calculations were based almost entirely on the rotational isomeric state (RIS) theory, but the possibility of using a Metropolis Monte Carlo method was also considered. Since the stiffness of the chains was of primary interest, the quantities calculated were the unperturbed dimensions and its temperature coefficient and the radii of gyration. Degrees of polymerization ranged from 40 to 400, and temperatures from 300 to 1000 K. The “characteristic ratio” (of the mean-square unperturbed dimensions to those of the corresponding freely-jointed chain) was found to be approximately 65 in the limit of very long chains. This is an order of magnitude larger than that of the much studied and very flexible poly(dimethylsiloxane), and the associated chain stiffness this indicates for PDPS seems to be consistent with its high transition temperatures and other properties.     

Corrections to scaling and crossover from good- to theta-solvent regimes of interacting polymers

We exploit known properties of universal ratios, involving the radius of gyration R(g), the second and third virial coefficients B(2) and B(3), and the effective pair potential between the centers of mass of self-avoiding polymer chains with nearest-neighbor attraction, as well as Monte Carlo simulations, to investigate the crossover from good- to theta-solvent regimes of polymers of finite length L. The scaling limit and finite-L corrections to scaling are investigated in the good-solvent case and close to the theta temperature. Detailed interpolation formulas are derived from Monte Carlo data and results for the Edwards two-parameter model, providing estimates of universal ratios as functions of the observable ratio A(2)=B(2)/R(g) (3) over the whole temperature range, from the theta point to the good-solvent regime. The convergence with L (L< or =8000) is found to be satisfactory under good-solvent conditions, but longer chains would be required to match theoretical predictions near the theta point, due to logarithmic corrections. A quantitative estimate of the universal ratio A(3)=B(3)/R(g) (6) as a function of temperature shows that the third virial coefficient remains positive throughout, and goes through a pronounced minimum at the theta temperature, which goes to zero as 1/ln L in the scaling limit.     

Moments and distribution function of polyelectrolyte chains

It is demonstrated that the moments R(2k) of the end-to-end distance distribution function f(r) of charged wormlike chains with excluded volume effects in solution with added salt, in the Debye-Huckel approximation, obey a remarkably simple relation. It is shown that the R(2k) can be expressed as weighted sums of the corresponding moments of ideal wormlike chains. As an application of this method, we show that the Fourier transform of f(r) can also be represented by a superposition of distribution functions of ideal chains. The quantities so calculated are compared with the results of Monte Carlo simulations. Excellent agreement between them is observed.     

Excluded volume effect for various chain models. II. Application to optical anisotropy and end-to-end distance of branched polymers

Monte Carlo simulation has been used to investigate the excluded volume problem for branched polymers. The mean-square optical anisotropy and mean-square end-to-end distance were examined for two models including short-range intramolecular interactions. Molecules of regular-comb and random-comb type were studied. The various effects found are discussed.     

聚亚甲基链的温度系数

本文采用旋转异构态模型,考虑排斥体积效应,用 Monte Carlo模拟方法计算了聚亚甲基高分子链的温度系数dln/dT。考虑排斥体积的聚亚甲基链的温度系数大于无扰聚亚甲基链的温度系数,并更接近实验值。     

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.     

Gel-permeation chromatography: Examination of universal calibration procedures for polydimethylsiloxane in a poor solvent

Various procedures for universal calibration in gel-permeation chromatography with polystyrene gels are examined for polystyrene and polydimethylsiloxane fractions. For o-dichlorobenzene at 138°C, experimental intrinsic viscosity–molecular weight data show that the Mark-Houwink exponents are 0.70 and 0.57 for polystyrene and polydimethylsiloxane, respectively. In principle, this difference permits a distinction between the various polymer size parameters proposed for universal calibration. An interpretation of the experimental polydimethylsiloxane calibration for o-dichlorobenzene at 138°C requires a consideration of errors in average molecular weights and errors arising from the use of average molecular weight instead of peak molecular weight. When calibration procedures utilizing hydrodynamic volume and unperturbed dimensions are examined, the difference between them is comparable with experimental error. If the Flory-Fox viscosity expression is employed, the perturbed end-to-end distance (or radius of gyration) and the hydrodynamic volume give equivalent universal calibrations. The experimental data are sufficiently accurate to show that the perturbed dimension determined with the Ptitsyn-Eizner relation does not give an adequate universal calibration.     

DYNAMIC MONTE CARLO STUDY ON THE CORRELATION BETWEEN SHAPE AND SIZE OF LINEAR POLYMER CHAINS

The correlation between shape and size of linear chains on the simple cubic lattice is investigated using a dynamicMonte Carlo technique. A positive correlation between the asphericity parameter A and the square of the end-to-end distanceR~2, as well as that between A and the square of the radius of gyration S~2, is found for both RW and SAW chains, indicatingthat a chain conformation of small size is usually more spherical than one of large size. The result can explain why the shapeof the SAW chain deviate much more from a sphere than that of the RW chain, and can also explain the similar dependenceof size and shape on chain stiffness and on the distance of the first bead of a chain from an infinitely large flat surface.     

Semi-empirical insertion probability for hard-spheres and hard-sphere chains

In spite of its simplicity and a well-defined theoretical basis, the Flory–Guggenheim approach is conventionally regarded as inapplicable to off-lattice system since the insertion probability of the approach does not account for the excluded region, existing in the off-lattice system. In this work, we propose the insertion probability accounting for the excluded region of off-lattice fluids and derive a new version of equation of state (EOS) for hard-sphere chains basing on the Flory–Guggenheim approach. To investigate the behavior of the excluded regions, a Monte Carlo sampling was performed for hard disks and the various excluded regions were found to have different density dependence. On the basis of the simulation result, we formulated the insertion probability for hard-sphere and that of hard-sphere chain which accounts for the effect of chain-connectivity on the monomer insertion. The proposed insertion probability was found to correctly predict the simulation data for monomer and correctly correlate the simulation data for chain fluids. The resulting EOS was found to meet closed-packed limit and predict the simulation data of compressibility factor for monomer and chains with a reasonable degree of accuracy. When compared with other off-lattice based EOS, it shows a comparable or better result. For second virial coefficient of chain molecules, the model was found to reasonably predict the simulation data.     

DIMENSIONS OF ATACTIC POLY（α-METHYLSTYRENE） CHAINS WITH SIDE GROUPS

An improved configurational-confomational statistical method is developed and the mean-square radius of gyration for atactic poly(α-methylstyrene)(PαMS)chains is studied,in which the effect of large side groups is considered. The deduced formulas,based on the rotational isomer state theory,are used to investigate the configuration-dependent properties of the atactic polymer chain,and the statistical correlation of the unperturbed polymer chain dimension and structure parameters are calculated.For the fraction of meso dyads w_m=0.4,the dependence of the radius of gyration R_g and the intrinsic viscosity[η]on the molecule mass M are R_g=2.63×10~(-2) M~(0.50) nm and[η]=7.36×10~(-2) M~(0.497),respectively, which are in agreement with the previous experimental data for the PαMS samples.A small hump is detected in the curve of the characteristic ratio of the unperturbed mean-square radius of gyration versus the chain length for short PαMS chains.The R_g increases linearly with the temperature T,and the effects of the chain length and the tacticity on the temperature coefficient are remarkable.These are quite different from the results for PαMS chains not considering side groups or for the monosubstituted polystyrene chain.