Conformational statistics of polymer chain terminally attached to wall (Ⅲ)——NRW model loop chain

When the two end groups of a linear polymer chain are absorbed on a solid surface,the polymer chain forms the "loop" conformation.Investigation has been made on the conformational statistics of a model loop chain by the normal landom walk (NRW) on a lattice confined in the half-infinite space.Based on the conformational distribution function of the NRW model tail chain,it is easy to deduce an analytical formula expressing the conforma-tional number of the model loop chain.It was found that the ratio of the conformational number of the model loop chain to that of the free chain varies with the power function N-2/3 when the chain length N→∞ The same result was obtained by means of the recursion equation.The ratio of the mean square end-to-end distance h2 for the model loop chain to its mean square bond length I2 is 2N/3 Compared with the free chain with the same length N,the mean square end-to-end distance of the model loop chain contracts to a certain extent.The basic relationships deduced were support     

Conformational statistics of polymer chain terminally attached to wall (I)——NRW model tail chain

The simplest form of a polymer chain adsorbed on a solid surface is that the polymer chain has only one end group attached to the surface, i.e. the polymer chain forms the "tail" conformation. In the present work, the problem was simplified as the random walk confined in the half-infinite space and studied systematically. The conformational distribution functions of the model tail chain in different dimensions were obtained. It has been found that the ratio of the conformational number of the model tail chains to that of the free chains varies as a power function N-12 when the chain length N→∞. It has also been proved that for the tail chain the component of the mean square end-to-end distance in the normal direction of the confined boundary is doubled and the other components are constant in comparison with the case of the free chain.     

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.     

A MONTE CARLO STUDY OF THE GLASS TRANSITION OF POLYMETHYLENE*

By this Monte Carlo simulation we studied the glass transition of polymethylene using themodified bond-fluctuation model combined with considering the rotational-isomeric state model. Theconfigurational properties in the polymethylene (PM) melts, such as the mean length, the mean energy perbond and the mean square radius of gyration were monitored. We found that the chains cannot be in theequilibrium states after a very long time when the temperature of the dense PM chains decreases to 120 K. Asthe melt vitrifies, these quantities gradually become independent of temperature in a narrow range. The glasstransition temperature T_g depends upon the chain length of PM chains, and extrapolation to (CH_2)_∞givesT_g~∞=212 K. The dynamics in the PM melts was also studied. It was found that the diffusion coefficients canbe described by the Vogel-Fulcher law and the Vogel-Fulcher temperature T_0 is 124 K. This method may beused to investigate the glass transition of other real polymer chains.     

MEAN-SQUARE RADIUS OF GYRATION AND DIPOLE MOMENT OF POLY(METHYLPHENYLSILOXANE) CHAINS

The mean-square radius of gyration ,the mean-square dipole moment ,the mean-square end-to-end distance and their temperature coefficients of unsymmetrical disubstituted poly(methylphenylsiloxane) (PMPS) chains, as a function of stereochemical structure,confomational energies and length of polymers,were studied by using an improved configurational-confomational statistical method based on the rotational-isomeric-state theory.It is found that the increase in isotacticity of PMPS chains caus...     

COMPUTER SIMULATION OF A SINGLE POLYMER CHAIN IN DIFFERENT SOLVENTS

In the present paper, the behavior of a single polymer chain under various solvent conditions was modeled by self-avoiding walks (SAW) with nearest neighbors attraction Δε on a simple cubic lattice. Determination of the θ-condition wasbased on the numerical results of the mean square radius of gyration and end-to-end distance. It was found that at the θtemperatue Δε/kT equals -0.27. The exponents a in the Mark-Houwink equation with different interaction parameters areconsistent with the results of experiments: under θ-condition, a = 0.5, and for a good solvent α= 0.74-0.84, respectively.     

THE SPATIAL DISTRIBUTION AND MOMENTS OF CIRCULAR FREELY JOINTED CHAIN

The spatial distribution function and second moments of circular freely jointed chain are derived based on an analytical method. The circular Gauss chain, which is simple for long chains, is compared with the circular freely jointed chain, which is exact for short chains. It is shown that the Gauss chain model predicts a more compact configurational distribution than the exact freely jointed chain. The two chain models, however, become closer to each other when the chain length increases. It is found that the difference of the mean square radius of gyration calculated with these two chain models is a constant, independent of the chain length.     

Analysis and Verification on the Chain-like Model with Normal Distribution of Magnetorheological Elastomer

Magnetorheological elastomer （MRE） is a new kind of smart materials, the rheological properties can be controlled rapidly by the external magnetic field. It is mainly composed of rubber and micron-sized ferromagnetic particles, which forms a chain-like structure. Therefore its mechanical, electric, and magnetic properties can be changed by the applied magnetic field, which is called as the magneto-induced effect. But this effect is not remarkable enough currently for the engineering application. So it is important for material preparation to optimize parameters to enhance the magneto-induced effect. In this work, based on chain-like model, some factors influencing the magneto-induced effect of MRE were analyzed theoretically by using dipole method with the normal distribution of chain＇s angle introduced. The factors included the oblique angle of particles chains, magnetic field intensity, and shear strain, etc. Some experiments were also carried out.     

Conformational elasticity theory of chain molecules

This paper develops a conformational elasticity theory of chain molecules, which is based on three key points: (i) the molecular model is the rotational isomeric state (RIS) model; (ii) the conformational distribution function of a chain molecule is described by a function of two variables, the end-to-end distance of a chain conformation and the energy of the conformation; (iii) the rule of changes in the chain conformational states during deformation is that a number of chain conformations would vanish. The ideal deformation behavior calculated by the theory shows that the change in chain conformations is physically able to make the upward curvature of the stress-strain curve at the large-scale deformation of natural rubber. With the theory, different deformation behaviors between polymers with different chemical structures can be described, the energy term of the stress in the deformations can be predicted, and for natural rubber the fraction of the energy term is around 13%, coinciding with the experi     

Stiffness and excluded volume effects on conformation and dynamics of polymers: A simulation study

This work investigates the effects of the excluded volume and especially those of the chain stiffness on the structural and dynamical properties of a model polymer chain.The theoretical framework is the same as in the recent works by Steinhauser et al.,where a Rouse approach is adopted.Our model differs in that our chains have a finite average bending angle.As in the works by Steinhauser et al.,Langevin dynamic simulations were performed without hydrodynamic interactions.Whereas this doesn’t impact the static properties we obtain,it also allows us to compare our results on dynamic properties to those predicted by Rouse theory,where hydrodynamic interactions are also neglected.Our results show that the structural properties are very sensitive to the chain stiffness,whereas the dynamic scaling laws remain the same as those by Rouse theory,with the prefactor depending on the persistence length.     

A Monte Carlo simulation study of the effect of chain length on the hydrolysis of poly(lactic acid)

Abstract The intrinsic relationship between molecular chain length and the probability of chain reaction during poly(lactic acid)(PLA)hydrolysis was investigated by Monte Carlo simulation.The chain reaction rate was calculated by introducing a power function of different molecular chain lengths.The hydrolysis of both amorphous and extended-chain crystal PLA was selected as the model system.It is found that,the chain reaction probability was proportional to the chain length with a power of 0.4 for amorphous PLA and 0.7 1 for extended-chain crystal PLA,respectively.These results indicate that PLA with longer chain length usually exhibits larger reaction rate than that with shorter length.Comparing the hydrolysis of the two kinds of PLA,the competition between longer and shorter chains in the different condensed structures is different.     

THE ADSORPTION OF LINEAR POLY(N-ISOPROPYLACRYLAMIDE)CHAINS ON SURFACTANT-FREE POLYSTYRENE NANOPARTICLES

The adsorption of linear poly(N-isopropylacrylamide) (PNIPAM) chains on surfactant-freepolystyrene (PS) nanoparticles was used as a model system to study the hydrophobic adsorption of polymeron the surface, because the hydrophobility of PNIPAM can be continuously varied by a small temperaturechange. The adsorption was investigated by a combination of static and dynamic laser light scattering (LLS)measurements, In static LLS, the absolute excess scattered light intensity led to the amount of PNIPAMadsorbed on the surface. In dynamic LLS, the hydrodynamic thickness of the adsorbed PNIPAM layer wasaccurately measured. For a given particle concentration, the adsorption increases as thc PNIPAMconcentration and the incubation temperature increase. The average density of the adsorbed PNIPAM layer isreciprocally proportional to the number of the PNIPAM chains on the surface, revealing a simple scaling ofthe chain density distribution. The adsorption follows the Langmuir's isotherm. The enthalpy changeestimated from the adsorption at 25℃and 30℃is slightly positive, indicating that the adsorption involvesthe coil-to-globule transition of the chains on the surface.     

Dynamics of polypropylene chains in their binary blends of different stereochemical sequences studied by Monte Carlo simulations

The conformational and dynamic properties of polypropylene （PP） for both pure melts and blends with different chain tacticity were investigated by Monte Carlo simulation of isotactic （iPP）, atactic （aPP） and syndiotactic （sPP） polypropylenes. The simulation of coarse-grained PP models was performed on a high coordination lattice incorporating short- and long-range intramolecular interactions from the rotational isomeric state （RIS） model and Lennard-Jones （LJ） potential function of propane pairs, respectively. The dynamics of chains in binary PP/PP mixture were investigated with the composition of C150H302 with different chain taciticity. The diffusion rates of PP with different stereochemistry are generally in the order as： iPP 〉 aPP 〉〉 sPP. For PP/PP blends with 50：50 wt% binary mixtures, immiscibility was observed when sPP was introduced into the mixtures. The diffusion rate of iPP and aPP became slower after mixing, while sPP diffuses significantly faster in the binary mixtures. The mobility of PP chains depends on both intramolecular （molecular size and chain stiffness） and intermolecular （chain packing） interactions. The effect of intramolecular contribution is greater than that of intermolecular contribution for iPP and aPP chains in binary mixtures. For sPP chain, intermolecular interaction has greater influence on the dynamics than intramolecular contribution.     

Diffusion and Relaxation Dynamics of Supercooled Polymer Melts

The dynamic properties of polymer melts are investigated in the range of normal liquid regime to the supercooled liquid regime. The polymer is modeled as a coarse-grained bead-spring model with chain length ranging from 5 to 160. The mean squared displacement and non-Gaussian parameter are used to describe the self diffusion of polymer beads. We find slow dynamics with decreasing temperature and increasing chain length. The time evolution of non-Gaussian parameters shows two peaks(or one peak one shoulder) in the α-relaxation time, τα, regime and sub-diffusion time regime, respectively, where the first primary peak indicates the dynamic heterogeneity stemmed from the motion of beads, and the secondary peak is the result of correlated motion along a polymer chain. Moreover, the relaxation of polymer beads shows clear two-step decay in supercooled melts and the dynamics shows growing heterogeneity with decreasing temperature. As chain length is increased, a peak of the dynamic susceptibility occurs, and the peak height,χ*4, increases and then reaches a plateau. The curves of the height of the first peak of α_2, α _2~*, versus τ and the curves of χ_4~*α versus τα follow two master curves for different chain lengths. Our results indicate the similarity of dynamic heterogeneity dominated by the motion of single bead even the chain length is different. It is interesting to find that the Stokes-Einstein(SE) relation between τα and diffusion coefficient D, D~τ-1 q, is highly length-scale dependent. The SE relation breaks down in both normal melts regime and supercooled regime at large magnitude of wave vectors, attributed to the non-Brownian motion arising from the chain connectivity and growing heterogeneity due to supercooling. However, the SE relation is reconstructed when the probing length scale is large(at small magnitude of wave vectors). Our results show a hierarchical physical picture of the supercooled polymeric dynamics.     

Probability Properties of Multi－contact in Protein Molecules

The compact conformations of polymers are important because the native conformations of all bio-polymers with certain function are highly compact. The properties of mutil-contact bio-polymer chains were studied by Gaussian statistics of the random-flight chain. The theoretical expressions(were given, also), the calculations of probability distributions and correlation functions for different topologic cases were derived and made respectively. Comparison between single, double and triple contacts was also made. By means of setting the parameters, the results of the current calculations of the multiple contacts are just the same as those calculated by single, double or tripe contacts separately. It is a useful method to investigate native conformations of biopolymers. The probabilities of multi contacts and correlation functions between chain‘s contacts were calculated for the Gaussian chains. Because the bond probability distributions are Gaussian‘s distributions, the probability distributions of the separations of various points along the chains are always consecutive. All the contacts may break up into several groups, and each group consists of many contacts. Here we investigated the probability distribution from one group to three groups of contacts.     

RATE OF INTRA-MOLECULAR CONTACT FORMATION IN SHORT TWO-DIMENSIONAL COMPACT POLYMERS CHAINS

It is important to know the rate of intra-molecular contact formation in proteins in order to understand how proteins fold clearly. Here we investigate the rate of intra-molecular contact formation in short two-dimensional compact polymer chains by calculating the probability distribution p(r) of end-to-end distance r using the enumeration calculation method and HP model on two-dimensional square lattice. The probability distribution of end-to-end distance p(r) of short two-dimensional compact polymers chains may consist of two parts, i.e. p(r) = p1(r) p2(r), where p1(r) and p2(r) are different for small r. The rate of contact formation decreases monotonically with the number of bonds N, and the rate approximately conforms to the scaling relation of k(N) ∝ N-α. Here the value of α increases with the contact radius a and it also depends on the percentage of H (hydrophobic) residues in the sequences of compact chains and the energy parameters of εHH, εHP and εPP . Some comparisons of theoretical predictions with experimental results are also made. This investigation may help us to understand the protein folding.     

A study on the structural transition of a single polymer chain by parallel tempering molecular dynamics simulation

The structural transition of a single polymer chain with chain length of 100,200 and 300 beads was investigated by parallel tempering MD simulation.Our simulation results can capture the structural change from random coil to orientationally ordered structure with decreasing temperature.The clear transition was observed on the curves of radius of gyration and global orientational order parameter P as the function of temperature,which demonstrated structural formation of a single polymer chain.The linear relationships between three components of square radius of gyration R_gx²,R_gx²,R_gz² and global orientational order P can be obtained under the structurally transformational process.The slope of the linear relationship between x（or y-axis） component R_gx²(or R_gy²) and P is negative,while that of RL as the function of P is positive.The absolute value of slope is proportional to the chain length.Once the single polymer chain takes the random coil or ordered configuration,the linear relationship is invalid.The conformational change was also analyzed on microscopic scale.The polymer chain can be treated as the construction of rigid stems connecting by flexible loops.The deviation from exponentially decreased behavior of stem length distribution becomes prominent,indicating a stiffening of the chain arises leading to more and more segments ending up in the trans state with decreasing temperature.The stem length N_tr is about 21 bonds indicating the polymer chain is ordered with the specific fold length.So,the simulation results,which show the prototype of a liquid-crystalline polymer chain,are helpful to understand the crystallization process of crystalline polymers.     

STUDY ON CASTOR OIL POLYURETHANE/POLY (METHYL METHACRYLATE) AB CROSSLINKED POLYMERS

Castor oil polyurethane/poly(methyl methacrylate) AB crosslinked polymers (ABCP) were synthesized by free radical copolymerization of MMA and vinyl-terminated castor oil polyurethane which was obtained from isocyanate-terminated castor oil polyurethane and hydroxyethyl methacrylate The mechanical properties, transition and relaxation, as well as compatibility and morphology of the ABCP were investigated by changing the component. The results show that the ABCP is a semicompatible system and the compatibility of the two components decreases with increasing content of the hard segment. The mechanical and damping properties of the ABCP are obviously superior to that of their homopolymers. The damping value is mainly controlled by cross[ink density of the ABCP but the T-g value by component.     

Conformational Properties of Comb-shaped Polyelectrolytes with Negatively Charged Backbone and Neutral Side Chains Studied by a Generic Coarse-grained Bead-and-Spring Model

A generic coarse-grained bead-and-spring model,mapped onto comb-shaped polycarboxylate-based(PCE)superplasticizers,is developed and studied by Langevin molecular dynamics simulations with implicit solvent and explicit counterions.The agreement on the radius of gyration of the PCEs with experiments shows that our model can be useful in studying the equilibrium sizes of PCEs in solution.The effects of ionic strength,side-chain number,and side-chain length on the conformational behavior of PCEs in solution are explored.Single-chain equilibrium properties,including the radius of gyration,end-to-end distance and persistenee length of the polymer backbone,shape-asphericity parameter,and the mean span dimension,are determined.It is found that with the increase of ionic strength,the equilibrium sizes of the polymers decrease only slightly,and a linear dependenew of the persistence length of backbone on the Debye screening length is found,in good agreement with the theory developed by Dobrynin.Increasing side-chain numbers and/or side-chain lengths increases not only the equilibrium sizes(radius of gyration and mean span)of the polymer as a whole,but also the persistence length of the backbone due to excluded volume interactions.