Scaling of the viscosity of the Lennard-Jones chain fluid model, argon, and some normal alkanes

In this work, we have tested the efficiency of two scaling approaches aiming at relating shear viscosity to a single thermodynamic quantity in dense fluids, namely the excess entropy and the thermodynamic scaling methods. Using accurate databases, we have applied these approaches first to a model fluid, the flexible Lennard-Jones chain fluid (from the monomer to the hexadecamer), then to real fluids, such as argon and normal alkanes. To enlarge noticeably the range of thermodynamics conditions for which these scaling methods are applicable, we have shown that the use of the residual viscosity instead of the total viscosity is preferable in the scaling procedures. It has been found that both approaches, using the adequate scaling, are suitable for the Lennard-Jones chain fluid model for a wide range of thermodynamic conditions whatever the chain length when scaling law exponents and prefactors are adjusted for each chain length. Furthermore, these results were found to be well respected by the corresponding real fluids.     

Influence of molecular topology on the static and dynamic properties of single polymer chain in solution

The influence of molecular topology on the structural and dynamic properties of polymer chain in solution with ring structure, three-arm branched structure, and linear structure are studied by molecular dynamics simulation. At the same degree of polymerization (N), the ring-shaped chain possesses the smallest size and largest diffusion coefficient. With increasing N, the difference of the radii of gyration between the three types of polymer chains increases, whereas the difference of the diffusion coefficients among them decreases. However, the influence of the molecular topology on the static and the dynamic scaling exponents is small. The static scaling exponents decrease slightly, and the dynamic scaling exponents increase slightly, when the topology of the polymer chain is changed from linear to ring-shaped or three-arm branched architecture. The dynamics of these three types of polymer chain in solution is Zimm-like according to the dynamic scaling exponents and the dynamic structure factors.     

Polymer translocation in solid-state nanopores: dependence of scaling behavior on pore dimensions and applied voltage

We investigate unforced and forced translocation of a Rouse polymer (in the absence of hydrodynamic interactions) through a silicon nitride nanopore by three-dimensional Langevin dynamics simulations, as a function of pore dimensions and applied voltage. Our nanopore model consists of an atomistically detailed nanopore constructed using the crystal structure of β-Si(3)N(4). We also use realistic parameters in our simulation models rather than traditional dimensionless quantities. When the polymer length is much larger than the pore length, we find the translocation time versus chain length scales as τ ～ N(2+ν) for the unforced case and as τ ～ N((1+2ν)/(1+ν)) for the forced case. Our results agree with theoretical predictions which indicate that memory effects and tension on the polymer chain play an important role during the translocation process. We also find that the scaling exponents are highly dependent on the applied voltage (force). When the length of the polymer is on the order of the length of the pore, we do not find a continuous scaling law, but rather scaling exponents that increase as the length of the polymer increases. Finally, we investigate the scaling behavior of translocation time versus applied voltage for different polymer and pore lengths. For long pores, we obtain the theoretical scaling law of τ ～ 1/V(α), where α ? 1 for all voltages and polymer lengths. For short pores, we find that α decreases for very large voltages and/or small polymer lengths, indicating that the value of α = 1 is not universal. The results of our simulations are discussed in the context of experimental measurements made under different conditions and with differing pore geometries.     

Scaling law of poly(ethylene oxide) chain permeation through a nanoporous wall

This paper presents a study of the permeation of poly(ethylene oxide) (PEO) chains through the nanoporous wall of hollow polymeric capsules prepared by self-assembly of polyelectrolytes. We employ the method of pulsed field gradient (PFG) NMR diffusion to distinguish chains in different sites, i.e., in the capsule interior and free chains in the dispersion, by their respective diffusion coefficient. From a variation of the observation time, the time scale of the molecular exchange between both sites and thus the permeation rate constant is extracted from a two-site exchange model. Permeation rate constants show two different regimes with a different dependence on chain length. This suggests a transition between two different mechanisms of permeation as the molecular weight is increased. In either regime, the permeation time can be described by a scaling law tau approximately N (b) , with b = (4)/ 3 for short chains and b = (1)/ 3 for long chains. We discuss these exponents, which clearly differ from the theoretical predictions for chain translocation.     

Kinetics of a semiflexible chain under external force

The kinetic properties of a semiflexible chain subject to an external force are investigated using scaling arguments and computer simulations. By monitoring the mean square displacements in principal axes, the authors found that the anisotropic dynamic fluctuations go through several distinct kinetic regimes characterized by two different exponents corresponding to transverse and longitudinal fluctuations. When a force is applied at one chain end, the tension propagates gradually to the other end, leading to nonuniform tension profiles. At short times, they observe sublinear relaxation of the mean square fluctuations in both longitudinal and transverse directions. At intermediate times, the kinetics is dominated by tension driven straightening with smaller kinetic exponents. Nonuniform tension profiles lead to the superlinear dependence of the longitudinal mean square displacement. In contrast, the late stage relaxation is diffusive again once the tension profile becomes uniform. The detailed tension profiles are reported for constant force measurement as well as constant pulling speed measurement.     

Markov chain modeling of polymer translocation through pores

We solve the Chapman-Kolmogorov equation and study the exact splitting probabilities of the general stochastic process which describes polymer translocation through membrane pores within the broad class of Markov chains. Transition probabilities, which satisfy a specific balance constraint, provide a refinement of the Chuang-Kantor-Kardar relaxation picture of translocation, allowing us to investigate finite size effects in the evaluation of dynamical scaling exponents. We find that (i) previous Langevin simulation results can be recovered only if corrections to the polymer mobility exponent are taken into account and (ii) the dynamical scaling exponents have a slow approach to their predicted asymptotic values as the polymer's length increases. We also address, along with strong support from additional numerical simulations, a critical discussion which points in a clear way the viability of the Markov chain approach put forward in this work.     

Integral equation theory for athermal solutions of linear polymers

An integral equation model is developed for athermal solutions of flexible linear polymers with particular reference to good solvent conditions. Results from scaling theory are used in formulating form factors for describing the single chain structure, and the impact of solvent quality on the chain fractal dimension is accounted for. Calculations are performed within the stringlike implementation of the polymer reference interaction site model with blobs (as opposed to complete chains) treated as the constituent structural units for semidilute solutions. Results are presented for the second virial coefficient between polymer coils and the osmotic compressibility as functions of the chain length and polymer volume fraction, respectively. Findings from this model agree with results from scaling theory and experimental measurements, as well as with an earlier investigation in which self-avoiding chains were described using Gaussian form factors with a chain length and concentration-dependent effective statistical segment length. The volume fractions at the threshold for connectedness percolation are evaluated within a coarse-grained closure relation for the connectedness Ornstein-Zernike equation. Results from these calculations are consistent with the usual interpretation of the semidilute crossover concentration for model solutions of both ideal and swollen polymer coils.     

Probing chain ends in adsorbed polymer layers

We study theoretically the pull-out of polymer chains from an adsorbed polymer layer by sticking of the chain ends on an opposing surface using scaling arguments and a mean field theory. When only one chain is pulled out from the layer, we extend previous results obtained for a single adsorbed chain and calculate the force necessary to extract the chain from the layer. We then discuss end adsorption from an adsorbed layer of polymers bearing specific end groups onto a second surface. Two bridging regimes are predicted: a diffuse layer regime at weak separations (or/and weak interaction) and a large separation strong interaction regime where the bridges stretch into a brush like structure. Bridging fractions and force profiles are displayed that could be compared to atomic force microscope or surface force apparatus experiments.     

Friction between brush layers of charged and neutral bottle-brush macromolecules. molecular dynamics simulations

Using molecular dynamics simulations, we study the lubricating properties of neutral and charged bottle-brush coatings as a function of the compression and shear stresses and brush grafting density. Our simulations have shown that in charged bottle-brush systems under shear there is a layer with excess counterions located in the middle between brush-bearing surfaces. The main deformation mode of the charged bottle-brush layers is associated with the backbone deformation, resulting in the backbone deformation ratio, α, and shear viscosity, η, being universal functions of the Weissenberg number. In the case of neutral bottle-brush systems, in addition to the backbone deformation there is also side chain deformation. The coupling between backbone and side chain deformation violates universality in the deformation ratio, α, dependence on the Weissenberg number and results in scaling exponents varying with the compression stress and brush grafting density. The existence of different length scales controlling deformation of neutral bottle brushes manifests itself in the shear viscosity, η, dependence on the shear rate, ?γ. Shear viscosity, η, as a function of the shear rate, ?γ, has two plateaus and two shear thinning regimes. The low shear rate plateau and shear thinning regime correspond to the backbone deformation, while the second plateau and shear thinning regime at moderate shear rates are due to side chain deformation. For both systems the value of the friction coefficient increases with increasing shear rate. The values of the friction coefficient for charged bottle-brush systems are about ten times smaller than corresponding values for neutral systems at the same shear rate.     

Finite-size scaling analysis on the phase transition of a ferromagnetic polymer chain model

The finite-size scaling analysis method is applied to study the phase transition of a self-avoiding walking polymer chain with spatial nearest-neighbor ferromagnetic Ising interaction on the simple cubic lattice. Assuming the scaling M2(T,n) = n(-2beta/nu)[phi0 + phi1n(1/nu)(T-T(c)) + O(n(2/nu)(T-T(c))2)] with the square magnetization M2 as the order parameter and the chain length n as the size, we estimate the second-order phase-transition temperature T(c) = 1.784 J/k(B) and critical exponents 2beta/nu approximately 0.668 and nu approximately 1.0. The self-diffusion constant and the chain dimensions (R2) and (S2) do not obey such a scaling law.     

A scaling analysis of the fracture mechanisms in glassy polymers

Recent experimental work on craze growth in polymers has shown that the reptation model for polymer motion may be successfully applied, in certain cases, to the behavior of glassy polymers in the solid phase. In this paper, a simple scaling analysis is presented to show how the primitive path model for reptation may be applied to the behavior of glassy polymers before and during slow crack growth. Different dynamic regimes are identified and related to the relaxation times of the polymer chain. The dependence on polymer chain length for each mechanism is described. Estimates for the fracture energy of each process are presented.     

端基附壁模型聚合物环形链的构象统计理论

环形链定义为两个端基均附壁的线形聚合物链所得的环 .采用精确计数和蒙特卡罗模拟方法 ,研究了自回避行走 (SAW)模型表示的环形链的构象 ,求得构象数和均方回转半径随链长的变化 .对于二维和三维SAW环形链 ,精确计数的最大链长分别为N =2 9和 1 9.用标度理论处理了数值结果 ,所得的标度指数和其他参数与理论预示值进行了比较 .模拟结果表明 ,SAW环形链限制壁平行方向的尺寸大于垂直方向的尺寸 ,与SAW尾形链尺寸的变化正好相反 .     

Statistical theory for hydrogen bonding fluid system of AaDd type (Ⅱ): Properties of hydrogen bonding networks

Making use of the invariant property of the equilibrium size distribution of the hydrogen bonding clusters formed in hydrogen bonding system of AaDd type, the analytical expressions of the free energy in pregel and postgel regimes are obtained. Then the gel free energy and the scaling behavior of the number of hydrogen bonds in gel phase near the critical point are investigated to give the corresponding scaling exponents and scaling law. Meanwhile, some properties of intermolecular and intramolecular hydrogen bonds in the system, sol and gel phases are discussed. As a result, the explicit relationship between the number of intramolecular hydrogen bonds and hydrogen bonding degree is obtained.     

Scaling laws in simple and complex proteins: size scaling effects associated with domain number and folding class

The native states of the most compact globular proteins have been described as being in the so-called “collapsed-polymer regime,” characterized by the scaling law R _g ~ n ^ν, where R _g is radius of gyration, n is the number of residues, and ν ≈ 1/3. However, the diversity of folds and the plasticity of native states suggest that this law may not be universal. In this work, we study the scaling regimes of: (i) one to four-domain protein chains, and (ii) their constituent domains, in terms of the four major folding classes. In the case of complete chains, we show that size scaling is influenced by the number of domains. For the set of domains belonging to the all-α, all-β, α/β, and α?+?β folding classes, we find that size-scaling exponents vary between 0.3?≤?ν?≤?0.4. Interestingly, even domains in the same folding class show scaling regimes that are sensitive to domain provenance, i.e., the number of domains present in the original intact chain. We demonstrate that the level of compactness, as measured by monomer density, decreases when domains originate from increasingly complex proteins.     

Statistical theory for hydrogen bonding fluid system of A_aD_d type(II):Properties of hydrogen bonding networks

Making use of the invariant property of the equilibrium size distribution of the hydrogen bonding clus- ters formed in hydrogen bonding system of AaDd type,the analytical expressions of the free energy in pregel and postgel regimes are obtained.Then the gel free energy and the scaling behavior of the number of hydrogen bonds in gel phase near the critical point are investigated to give the corre- sponding scaling exponents and scaling law.Meanwhile,some properties of intermolecular and in- tramolecular hydrogen bonds in the system,sol and gel phases are discussed.As a result,the explicit relationship between the number of intramolecular hydrogen bonds and hydrogen bonding degree is obtained.     

Dependence on chain length of NMR relaxation times in mixtures of alkanes

Many naturally occurring fluids, such as crude oils, consist of a very large number of components. It is often of interest to determine the composition of the fluids in situ. Diffusion coefficients and nuclear magnetic resonance (NMR) relaxation times can be measured in situ and depend on the size of the molecules. It has been shown [D. E. Freed et al., Phys. Rev. Lett. 94, 067602 (2005)] that the diffusion coefficient of each component in a mixture of alkanes follows a scaling law in the chain length of that molecule and in the mean chain length of the mixture, and these relations were used to determine the chain length distribution of crude oils from NMR diffusion measurements. In this paper, the behavior of NMR relaxation times in mixtures of chain molecules is addressed. The author explains why one would expect scaling laws for the transverse and longitudinal relaxation times of mixtures of short chain molecules and mixtures of alkanes, in particular. It is shown how the power law dependence on the chain length can be calculated from the scaling laws for the translational diffusion coefficients. The author fits the literature data for NMR relaxation in binary mixtures of alkanes and finds that its dependence on chain length agrees with the theory. Lastly, it is shown how the scaling laws in the chain length and the mean chain length can be used to determine the chain length distribution in crude oils that are high in saturates. A good fit is obtained between the NMR-derived chain length distributions and the ones from gas chromatography.     

Critical dynamics of ballistic and Brownian particles in a heterogeneous environment

The dynamic properties of a classical tracer particle in a random, disordered medium are investigated close to the localization transition. For Lorentz models obeying Newtonian and diffusive motion at the microscale, we have performed large-scale computer simulations, demonstrating that universality holds at long times in the immediate vicinity of the transition. The scaling function describing the crossover from anomalous transport to diffusive motion is found to vary extremely slowly and spans at least five decades in time. To extract the scaling function, one has to allow for the leading universal corrections to scaling. Our findings suggest that apparent power laws with varying exponents generically occur and dominate experimentally accessible time windows as soon as the heterogeneities cover a decade in length scale. We extract the divergent length scales, quantify the spatial heterogeneities in terms of the non-Gaussian parameter, and corroborate our results by a thorough finite-size analysis.     

Conformational statistics of polymer chain terminally attached to wall (II)

The SAW tail chains were studied. The permitted conformational number and the mean square end-to-end distance as a function of the chain length N for such a model tail chain were obtained by computer simulations, including the exact enumeration and Monte Carlo method. These two basic quantities obeyed the relations deduced from the scaling law. The critical exponents and the lattice indexes were given by fitting the data of the computer experiments. It has been shown that there is a certain extension in the size of the SAW tail chains as well as the NRW tail chains in the direction normal to the wall. The normal component of the mean square end-to-end distance is almost twice as large as the parallel component of the short chain SAW. However, as N →∞, the effect of the wall on the chain conformation becomes a little weak because of the self-avoiding behavior for the model. That is quite different from the case of the NRW tail chain. Project supported by the National Natural Science Foundation of China     

金刚石格点上自避行走尾形链的构象统计理论

研究了金刚石格点上自避随机行走（ＳＡＷ）尾形链，采用精确计数和ＭｏｎｔｅＣａｒｌｏ模拟方法求得该ＳＡＷ尾形链的构象数Ｃ（Ｄ）１（Ｎ）和均方末端距［ｈ（Ｄ）１（Ｎ）］２及其分量随链长Ｎ的变化关系．发现它们与自由ＳＡＷ链一样都服从标度律，从这些量的计算机实验数据拟合求出了金刚石格点上ＳＡＷ尾形链的临界指数和格点指数．计算结果还表明短链ＳＡＷ在壁的法向与ＮＲＷ尾形链一样有所伸展，均方末端距的法向分量几乎是平行分量的２倍；但随Ｎ→∞，链自回避效应对壁的作用有所屏蔽．这些都与简立方格子模型上得到的结果一致．     

Rheology of concentrated carbon nanotube suspensions

The rheological properties of non-Brownian carbon nanotube suspensions are measured over a range of nanotube volume fractions spanning the transition from semidilute to concentrated. The polymer-stabilized nanotubes are "sticky" and form a quiescent elastic network with a well-defined shear modulus and yield stress that both depend strongly on nanotube volume fraction with different but related critical exponents. We compare controlled-strain-rate and controlled-stress measurements of yielding in shear flow, and we study the effect of slow periodic stress reversal on yielding and the arrest of flow. Our measurements support a universal scaling of both the linear viscoelastic and steady-shear viscometric response. The former allows us to extract the elastic shear modulus of semidilute nanotube networks for values that are near or below the resolution limit of the rheometers used, while the latter provides a similar extrapolation of the yield stress. A simple scaling argument is used to model the dependence of yield stress and elastic modulus on concentration.