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.     

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...     

Elastic behavior of comb-like polymer chains

<正>Three-dimensional Monte Carlo simulations of comb-like polymer chains with various backbone lengths N_b,arm lengths N_a and arm densities m are carried out to study the elastic behavior of comb-like polymer chains.The radius of gyration,the shape factors and bond length in different cases during elastic process are calculated,and it is found that the comb-like polymer molecules with longer backbone or shorter arm are more close to linear chains.But the arm density m affects the chain conformation non-monotonously.Some thermodynamic properties are also studied.Average Helmholtz free energy and elastic force f all increase with elongation ratioλfor all chains.     

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.     

Simulation Study on the Extension of Semi-flexible Polymer Chains in Cylindrical Channel

The scaling relations among the mean end-to-end distance of polymer along the channel R_(||), the polymer length N, and the effective diameter of channel De were investigated for flexible and semi-flexible polymer chains confined in long cylindrical channels. For the flexible polymer chain, scaling relation R_(||) ～ ND_e–0.7 was found in the classic de Gennes regime at l_p~2/b D_e R_g with l_p the persistence length, b the bond length, and Rg the radius of gyration of polymer. For the semi-flexible polymer, R_(||) ～ NDe–1 in the transition regime l_p D_e xl_p(x 1) and R_| ～ D_e–0.7 in the classic de Gennes regime at larger D_e xl_p were observed. The simulation results revealed that the scaling relation in the transition regime was due to the rod-like behavior of the semi-flexible polymer in the small regime l_p D_e xl_p.     

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.     

ORDERED STRUCTURAL EVOLUTION AND RELAXATION BEHAVIORS OF A SERIES MICROPHASE SEPARATED “HAIRY-ROD” POLYIMIDES WITH MULTIPLE ALKYL SIDE CHAINS

A series of “hairy-rod” polyimides, BBPA(n), with multiple alkyl side chains was prepared from 3,3′,4,4′-biphenyltetracarboxylic dianhydride (BPDA) and 4,4′-biphenyldiamine substituted in the 2,2′-positions with benzoate, which was substituted in the 3,4,5-positions with ether side chains of varying lengths. The number of the methylene units, n, in these alkyl side chains were in even numbers ranging from 8 to 18. Combining techniques of one-dimensional (1D) and 2D wide angle x-ray diffraction, 1D small angle X-ray scattering, differential scanning calorimetry experiments, it was found that this series of “hairy-rod” polyimides possess a micro-phase separation between the backbones and side chains. This led to the formation of ordered structures in two different length scales, of which both are hexagonal packing: one is attributed to the alkyl side chains on the sub-nanometer scale, and another is for the whole polymer chains on the nanometer scale. The development of the hexagonal structure on the sub-nanometer scale was critically dependent upon the lengths of the alkylside chains. Three relaxation processes were captured by dynamic mechanical analysis, i.e., segmental motion of the backbones, α the melting of the side chain crystals, β1, which exits only for the materials with longer side chains(n=18,16); and the subglass relaxation of side chains, β2- The peak relaxation temperature of the α process decreased with increasing the length of side chains, while the one of the β2 process increased. The activation energy of the α relaxation was relatively independent on the length of side chain, whereas, β2 process showed the increasing of activation energy with increasing the length of side chains.     

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.     

ORDERED STRUCTURAL EVOLUTION AND RELAXATION BEHAVIORS OF A SERIES MICROPHASE SEPARATED "HAIRY-ROD" POLYIMIDES WITH MULTIPLE ALKYL SIDE CHAINS

A series of "hairy-rod" polyimides, BBPA(n), with multiple alkyl side chains was prepared from 3,3′,4,4′biphenyltetracarboxylic dianhydride (BPDA) and 4,4′-biphenyldiamine substituted in the 2,2′-positions with benzoate, which was substituted in the 3,4,5-positions with ether side chains of varying lengths. The number of the methylene units, n, in these alkyl side chains were in even numbers ranging from 8 to 18. Combining techniques of one-dimensional (1D) and 2D wide angle x-ray diffraction, 1D small angle X-ray scattering, differential scanning calorimetry experiments, it was found that this series of "hairy-rod" polyimides possess a micro-phase separation between the backbones and side chains. This led to the formation of ordered structures in two different lengthscales, of which both are hexagonal packing: one is attributed to the alkyl side chains on the sub-nanometer scale, and another is for the whole polymer chains on the nanometer scale. The development of the hexagonal structure on the sub-nanometer scale was critically dependent upon the lengths of the alkyl side chains. Three relaxation processes were captured by dynamic mechanical analysis, i.e., segmental motion of the backbones, α, the melting of the side chain crystals, β1, which exits only for the materials with longer side chains (n = 18,16); and the subglass relaxation of side chains,β2. The peak relaxation temperature of the α process decreased with increasing the length of side chains, while the one of theβ2 process increased. The activation energy of the αrelaxation was relatively independent on the length of side chain, whereas, β2 process showed the increasing of activation energy with increasing the length of side chains.     

Probing relationship between structure and viscosity of unentangled polymers in steady shear flow

Structural responses of unentangled polymers of various architectures, including linear, ring, star, asymmetric star, and H-shaped polymers, in steady shear flow are investigated via nonequilibrium molecular dynamics simulations. As observed in our previous simulations, these polymers, when having an identical equilibrium mean-square radius of gyration R_(g0)~2 exhibit the same viscosity curve in both the linear and nonlinear regimes. In this article, the polymer orientation and deformation and the rate of deformation are calculated as a function of shear rate. The differences between different architectures in most of these properties are found to be related to the polymer extensibility, the number of free ends and the ability of folding. The unique architecture-independent quantity is the gradient component G_(yy) of the radius of gyration tensor. We find that a simple relation η=C_ηR_(g0)~2(3G_(yy)/R_(g0)~2)~(3/2) gives a near-perfect fit to shear viscosity η data, where C_η is a constant. The results suggest that this relation between chain thickness and viscosity is universal for unentangled polymers of various architectures.     

ROLE AND IMPORTANCE OF RADIUS OF GYRATION OF CHAINS IN THE MELT IN THE CRYSTALIZATION OF POLY(1-BUTENE)

Crystallization in polymer systems actually is a process that transfers the entangled melts into a semi-crystallinelayered structure. Whether or not a chain disentangles may result in different crystallization mechanism. When compared tothe crystal thickness (d_c), the volume occupied by the chain in the melt, i.e., the radius of gyration (R_g), plays a veryimportant role in polymer crystallization. When d_c≤R_g, crystallization does not necessitate a chain disentangling. Theentanglements are just shifted into the amorphous regions. However, as d_c>R_g, i.e., as the crystal thickness ges larger thanthe radius of gyration of the chain in the melt, it becomes necessary for a chain to disentangle. Then a change ofcrystallization mechanism occurs. Such change has been experimentally observed in the crystallization of poly(1-butene). Achange in the crystal morphologies from spherulite to quadrangle, is seen via PLM, as crystalliation temperatures increase.Even more, such a change is molecular weigh dependent and shifts to lower temperature as molecular weigh decreases.There exists a jump of crystal thickness and crystallinity associated with morphological change, as seen via SAXS. A changeof crystallization kinetics and crystallinity is further evidenced via dilatometry. The unique feature of P1b crystallization hasbeen discussed based on the radius of gyration of chain in the melt (R_g), and very good agreement is obtained.     

Alkoxy substituted benzodithiophene-alt-fluorobenzotriazole copolymer as donor in non-fullerene polymer solar cells

A new benzodithiophene(BDT)-alt-fluorobenzotriazole(FBTA) D-A copolymer J40 was designed and synthesized by introducing 2-octyldodecyloxy side chains on its BDT units, for expanding the family of the BDT- alt-FBTA-based copolymers and investigating the side chain effect on the photovoltaic performance of the polymer in non-fullerene polymer solar cells(PSCs).J40 exhibits complementary absorption spectra and matched electronic energy levels with the n-type organic semiconductor(n-OS)(3,9-bis(2-methylene-(3-(1,1-dicyanomethylene)-indanone))-5,5,11,11-tetrakis(4-hexylphenyl)-dithieno[2,3-d:2′,3′-d′]-sindaceno[1,2-b:5,6-b′]dithiophene)(ITIC) acceptor, and was used as polymer donor in the non-fullerene PSCs with ITIC as acceptor. The power conversion efficiency(PCE) of the PSCs based on J40:ITIC(1:1, w/w) with thermal annealing at 120 °C for 10 min reached 6.48% with a higher open-circuit voltage(Voc) of 0.89 V. The high Voc of the PSCs is benefitted from the lower-lying highest occupied molecular orbital(HOMO) energy level of J40. Although the photovoltaic performance of the polymer J40 with alkoxy side chain is lower than that of J60 and J61 with alkylthio-thienyl conjugated side chains, the PCE of6.48% for the J40-based device is still a relatively higher photovoltaic efficiency in the non-fullerene PSCs reported so far. The results indicate that the family of the BDT-alt-FBTA-based D-A copolymers are high performance polymer donor materials for non-fullerene PSCs and the side chain engineering plays an important role in the design of high performance polymer donors in the non-fullerene PSCs.     

SHAPE OF POLYMER CHAINS ON A TETRAHEDRAL LATTICE*

The shape of unperturbed polymer chains was studied using the Monte Carlo technique on a tetrahedral lattice.The asphericity A, the ratios/and/ were calculated for different values of polymer chain length n,conformational energy ε (ε≥0) and temperature T. The asphericity A decreases with the increase of chain length and tends toreach its limiting value rapidly with the decrease of γ(γ=ε/k_BT). For large n, A is about 0.525±0.005, the ratios/ and/ are about 2.7 and 12.0, respectively, and are almost independent of γ, but for short chains, theydepend on γ.     

A steered molecular dynamics simulation on the elastic behavior of adsorbed star polymer chains

<正>Elastic behavior of 4-branched star polymer chain with different chain length N adsorbed on attractive surface is investigated using steered molecular dynamics(SMD) simulation method based on the united-atom(UA) model for branched alkanes.The simulation is realized by pulling up the chain via a linear spring with a constant velocity v = 0.005 nm/ps.At the beginning,the chain lies extensionally on adsorbed surface and suffers continuous deformations during the tensile process.Statistical parameters as mean-square radii of gyration S~2_(xy),S~2_z,shape factor δ,describing the conformational changes,sectional density den which gives the states of the chain,and average surface attractive energy U_a,average total energy U,average force f probed by the spring,which characterize the thermodynamic properties, are calculated in the stimulant process.Remarkably,distinguishing from the case in linear chains that there only exists one long plateau in the curve of f,the force plateau in our study for star chains is multiple,denoting different steps of desorption,and this agrees well with the experimental results in essence.We find during the tensile process,there are three characteristic distances Z_c,Z_t and Z_0 from the attractive surface,and these values vary with N.When Z=Z_c,the chain is stripped from the surface,but due to the form of wall-monomer interaction,the surface retains weak influence on the chain till Z = Z_c.From Z=Z_t,parameters U_a,U and f respectively reach a stable value,while the shape and the size of the chain still need adjustments after Z_t till Z_0 to reach their equilibrium states.Specifically,for short chain of N= 41,Z_t and Z_0 are incorporated.These results may help us to deepen the knowledge about the elastic behavior of adsorbed star polymer chains.     

Curing theory of A_f-A_g type free radical polymerization (Ⅱ)——Characterization of network structural parameters

By means of the polymer statistical theory, the A_f-A_g type nonlinear free radical polymerization is investigated to give the number of effective elastic chains, the number of effective elastic mers and the average length for the elastic chains. The corresponding quantities for the dangling chains, the number of effective cross-linkage and the modulus are also obtained. Furthermore, the number- and weight-fractions of elastic chains are deduced.     

ADSORPTION OF SHORT TWO-DIMENSIONAL COMPACT CHAINS

Short two-dimensional compact chains adsorbed on the attractive surface at different temperatures were investigated by using the enumeration calculation method. First we investigate the chain size and shape of adsorbed chains, such as characteristic ratios of mean-square radii of gyration 〈S^2〉x/N and 〈S^2〉y/N, shape factor 〈δ〉, and the orientation of chain bonds 〈cos^2 θ〉 to illuminate how the size and shape of adsorbed compact chains change with increasing temperatures. There are some special behaviors for the chain size and shape at low temperature, especially for strong attraction interaction. In the meantime, adsorbed compact chains have different behaviors from general adsorbed polymer chains. Some thermodynamics properties are also discussed here. Heat capacity changes non-monotonously, first increases and then reduces. The transition temperature Tc is nearly 1.0, 1.4, 2.0 and 4.2 （in the unit of To） for the case of ε = 0, -1, -2 and -4 （in the unit of kTo）, respectively. Average energy per bond increases while average Helmholtz free energy per bond decreases with increasing temperatures. From these two thermodynamics parameters we can also get another transition temperature Tc＇, and it is close to 0.7, 1.1, 1.5 and 3.4 for ε= 0, -1, -2, and -4, respectively. Therefore, Tc is greater than Tc＇ under the same condition. These investigations may provide some insights into the thermodynamics behaviors of adsorbed protein-like chains.     

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.     

Donor-Acceptor Oligomers and Polymers Composed of Benzothiadiazole and 3-Hexylthiophene： Effect of Chain Length and Regioregularity

A series of donor-acceptor oligomer OBTThn （n = 1- 7） and polymer PBTThl and PBTTh2 composed of al- ternative 2,1,3-benzothiadiazole and 3-hexylthiophene have been designed and synthesized for the purpose of in- vestigation on the effect of chain length and side-chain regioregularity on their basic properties and photovoltaic performance. In the OBTThn oligomers and PBTThl polymer, all the hexyl side chains on thienyl units orient to- ward the same direction. Upon elongation of the chain length, the intramolecular charge transfer （ICT） absorption band in solution gradually redshifts from 398 nm for OBTThl to 505 nm for OBTThT, then to 512 nm for PBTThl polymer. Meanwhile, the HOMO energy level increases from -5.45 eV （OBTTh0 to -5.08 eV （OBTThT） and -5.09 eV （PBTThl）, and the LUMO energy level decreases from -3.11 eV （OBTTh0 to -3.30 eV （OBTThT） and -3.33 eV （PBTThl）, thus giving a smaller and smaller energy bandgap for higher oligomers and polymers. Theo- retical calculation suggests straight line-like backbone geometry for this series of oligomers and polymer. On the other hand, polymer PBTTh2 possesses a different side-chain regioregularity, in which every two neighbor hexyl side chains are arranged in different orienting direction. It is theoretically suggested to have curved line-like back- bone geometry. In solution, it shows similar photophysical and electrochemical properties as PBTThl. However in film state, it displays a less redshift in the ICT band as refer to that in solution than PBTThl. In combination with [6,6]-phenyl-C61-butyric acid methyl ester （PC61BM）, these oligomers and polymers were used as donor material to fabricate organic bulk heterojunction solar cells. Again, chain length-dependent device photovoltaic performance was observed. The device based on OBTTh4 showed a power conversion efficiency of 0.16%, while it increased to 0.36% and 0.49% for the devices based on OBTTh6 and PBTThb respectively. However, the side-chain regio- regularity has less influence on the device photovoltaic output since the device based on PBTTh~ displayed an effi- ciency of 0.52%, comparable to that of PBTThl.     

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.