三维吸附紧密高分子单链的力学性质研究

采用PERM(pruned-enriched Rosenbluth method)算法,研究了吸附在界面附近的紧密高分子链力学行为.发现当界面的吸附能比较大时,紧密高分子链从紧贴于吸附界面到逐渐远离的过程中,其外形会经历4种典型的变化.同时紧密高分子链的尺寸大小如/N、xy/N、z/N,形状参数<δ*>,热力学性质如每个键的平均自由能A/N,平均相互作用能/N等,甚至所受外力的大小都会同时做出相应的变化,其出现变化的位置也一致.特别是随着紧密高分子链离开吸附界面的过程中,作用于高分子链上的外力明显出现几个力学平台,这与实验得到的结果完全一致.同时还研究了弱吸附能的情况,在这种情况下实验是很难进行的.     

Elastic behavior of adsorbed polymer chains

Elastic behaviors of single polymer chains adsorbed on the attractive surface are first investigated using Monte Carlo simulation method based on the bond fluctuation model. We investigate the chain size and shape of adsorbed chains, such as mean-square radius of gyration S2, mean-square bond length b2, shape factors sf(i) and delta*, and the orientation of chain segments P2, to illuminate how the shape of polymer chains changes during the process of tensile elongation. There are some special behaviors of the chain size and shape at the beginning of elongation, especially for strong attraction interaction. For example, mean fraction of adsorbed segments decreases abruptly in the region of small elongation ratio and then decreases slowly with increasing elongation ratio. In fact, the chain size and shape also changes abruptly for small elongation ratio with strong attraction interaction. Some thermodynamics properties are also investigated here. Average Helmholtz free energy increases fast for elongation ratio lambda<1.15, especially with strong attraction, and increases slowly for lambda>1.15. Similar behaviors are obtained for average energy per bond. Elastic force (f ) and energy contribution to force (f(U)) are also studied, and we find that elastic force decreases abruptly for lambda<1.15, and there is a minimum of elastic force for strong attraction interaction, then increases very slowly with increasing elongation ratio. However, there are different behaviors for weak attraction interaction. For energy contribution to force (f(U)), there is a maximum value for strong attraction interaction in the region of lambda<1.15. Some comparisons with the atomic force microscopy experiments are also made. These investigations may provide some insights into the elastic behaviors of adsorbed polymer chains.     

ELASTIC BEHAVIOR OF PROTEIN-LIKE SINGLE CHAIN

The conformational properties and elastic behaviors of protein-like single chains in the process of tensile elongation were investigated by means of Monte Carlo method. The sequences of protein-like single chains contain two types of residues: hydrophobic (H) and hydrophilic (P). The average conformations and thermodynamics statistical properties of protein-like single chains with various elongation ratio λ were calculated. It was found that the mean-square end-to-end distance r increases with elongation ratio,λ. The tensor eigenvalues ratio of : decreases with elongation ratio λ for short (HP)x protein-like polymers, however, the ratio of : increases with elongation ratioλ,especially for long (H)x sequence. Average energy per bond increases with elongation ratioλ, especially for(H)x protein-like single chains. Helmholtz free energy per bond also increases with elongation ratioλ. Elastic force (f), energy contribution to force (fU) and entropy contribution to force (fs) for different protein-like single chains were also calculated.These investigations may provide some insights into elastic behaviors of proteins.     

Elastic behavior of short compact chains confined in double parallel boundaries

Adsorption of short two-dimensional compact chains confined in the double attractive parallel planar boundaries is investigated by using enumeration calculation method in this paper. First, we calculate the chain size and shape of adsorbed compact chains, such as mean-square end-to-end distance per bond R²/N, mean-square radii of gyration per bond S²_x/N and S²_y/N, shape factor δ and fraction of adsorbed segments f_a to illuminate that how the size and shape of adsorbed compact chains changes during the process of tensile elongation. There are some special behaviors in the chain size and shape for strong attraction interaction. In the meantime, compact chains can reach to the stable state with large distance between two parallel boundaries D. On the other hand, some thermodynamic properties, such as average energy per bond, Helmholtz free energy per bond, elastic force f and energy contribution to elastic f_U are also investigated in order to study the elastic behavior of compact chains adsorbed on the double attractive parallel planar boundaries. These investigations may provide some insights into the thermodynamic behaviors of adsorbed compact chains.     

EFFECTS OF SECONDARY STRUCTURE ON ELASTIC BEHAVIOR OF PROTEIN-LIKE CHAINS

The elastic behavior of protein-like chains was investigated by using the Pruned-Enriched-Rosenbluth Method (PERM).Three typical protein-like chains such as all-α,all-β,and α+β(α/β) proteins were studied in our modified orientation dependent monomer-monomer interaction (ODI) model.We calculated the ratio of /N and shape factor <δ*> of protein-like chains in the process of elongation.In the meantime,we discussed the average energy per bond ＜U＞/N,average contact energy per bond ＜U＞c/N,average helical energy per bond ＜U＞h/N and average sheet energy per bond ＜U＞b/N.Three maps of contact formation,α-helix formation,β-sheet formation were depicted.All the results educe a view that the helix structure is the most stable structure,while the other two structures are easy to be destroyed.Besides,the average Helmholtz free energy per bond ＜A＞/Nis was presented.The force f obtained from the free energy was also discussed.It was shown that the chain extended itself spontaneously first.The force was studied in the process of elongation.Lastly,the energy contribution to elastic force fu was calculated too.It was noted that fu for all-β chains increased first,and then decreased with x0 increasing.     

类蛋白质分子的二级结构对力学行为的影响

采用Kolinski等建立的类蛋白质分子的格点模型,研究了由典型的(HHPPHPP)x重复单元构成、含有α螺旋结构的类蛋白质分子链在拉伸过程中的构象性质和力学行为.发现不同强度的α螺旋相互作用会直接影响其拉伸过程.α螺旋相互作用强的类蛋白质分子链,具有更低的内能,更小的应力,在拉伸过程中更容易失去紧密接触对,同时也更容易被拉成“棒状”结构,但在整个拉伸过程中,α螺旋结构且能保持稳定;还发现类蛋白质分子的链长对拉伸也有影响,对较长的类蛋白质分子链,其内能更低,弹性力更小,自由能更大,紧密接触对的含量比例也更高,而“棒状化”程度较小.这些研究能够帮助我们加深对蛋白质分子的构象和弹性力学行为的理解.     

Elastic behavior of single polymer chains adsorbed on rough surfaces

In this paper, elastic behaviors of single polymer chains adsorbed on the rough surfaces with a substrate and some periodically tactic pillars are investigated by the pruned-enriched-Rosenbluth method (PERM). In our simulation, a single polymer chain is firstly adsorbed on the substrate and then pulled along the z-axis direction, which is vertical to the substrate. We investigate the chain size and shape of polymer chains, such as mean-square radii of gyration per bond 〈S²〉_xy/N, 〈S²〉_z/N and shape factor 〈δ^∗〉 in order to show how the size and shape of adsorbed polymer chains change during the desorption process. Due to the occurrences of separation of the chains from the substrate, farther adsorption on the upper surfaces of pillars and complete separation from the whole rough surfaces in the elastic process, the changes of 〈S²〉_xy/N, 〈S²〉_z/N and 〈δ^∗〉 during the process are complicated. On the other hand, some thermodynamic properties such as average energy per bond, average Helmholtz free energy per bond, elastic force f are investigated, and our aim is to study the elastic behaviors of polymer chains adsorbed on the rough surface during the elasticity process. Elastic force f has some plateaus during the desorption process for strong adsorption interaction. If there is no adsorption interaction, the chains can get away from the rough surfaces spontaneously. These investigations can provide some insights into the elastic behaviors of polymer chains adsorbed on the rough surface.     

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 structures and thermodynamic properties of compact polymer chains confined between two parallel plane boundaries

In this paper, the authors investigated the adsorption phenomenon of compact chains confined between two parallel plane boundaries using a pruned‐enriched Rosenbluth method. The authors considered three cases with different adsorption energies of ε = 0, ?1, and ?3 (in units of k_BT) for the confined compact chains of different chain lengths N, respectively. Several parameters were employed to describe the size and shape of compact chain, and some special behaviors in the conformational structures were investigated for the first time. For example, the size and shape of confined compact chains undergo distinct changes in the adsorption cases of ε = ?1 and ?3, and pass through the maximum values at the characteristic distances D_c. The authors found that this characteristic distance D_c could be scaled as D_c～ (N + 1)^ν (ν = 0.56 ± 0.01) in the case of ε = ?3. In addition, the microstructures of chains were investigated, and several significant results were obtained by analyzing the segment density distribution and the mean fractions of segment in tails, trains, bridges, and loops structures. On the other hand, the thermodynamic properties were also investigated for the confined compact chains, such as average energy per bond, Helmholtz free energy per bond, and elastic force per bond. Results show that elastic forces f have different behaviors in three cases, indicating that it is not necessary to exert an external force on the boundaries in the nonadsorption case. At the same time, the average contact energy of compact chain obviously changes when the distance between the two parallel boundaries D increases, which is similar to those of the size and shape parameters. The authors also conclude that these thermodynamic properties of compact chains depend strongly on not only the adsorption energies but also the chain lengths and the confined condition. In addition, several results of the conformational and thermodynamic parameters, such as the segment density distribution and free energy, were compared with the results from the self‐consistent field theory. These investigations may help us to deepen the knowledge about the adsorption phenomenon of confined compact chains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2888–2901, 2006     

Elastic behavior of short compact polymers

In this paper, we investigate the elastic behaviors of short compact polymers using the enumeration calculation method and the HP model on a two-dimensional square lattice. Both the mean-square end-to-end distance R(2) and the ratio of R(2)/S(2) increase with lambda. However, when the elongation ratio becomes larger, the curves of R(2)/S(2) become smooth and they are close to the limit of 10.50 for different compact polymers. We also investigate the changes of interior conformations in the process of tensile elongation through calculating the probabilities of three bond angles (i.e., 90 degrees, 180 degrees, and 270 degrees). The average energy and Helmholtz free energy per bond are both negative and increase with elongation ratio lambda. In the meantime, the elastic force per bond (f ) also increases with elongation ratio lambda, and the energy contribution to the elastic force (f(U)) increases first and then drops, and there exists the maximum of f(U) in the region of lambda=1.40-1.80 for different sequences. The entropy contribution to force (f(S)) is close to zero at a small elongation ratio lambda and then increases with lambda. Some comparisons with different sequences (including nonfolding and folding sequences) are also made.     

Elastic behavior of non-Gaussian polymethylene chains

In this paper, elastic behaviors of non-Gaussian polymethylene (PM) chains with chain length N=100 are investigated by rotational isomeric state model. Here the tetrahedral lattice of PM chain and the non-local interaction of Sutherland potential are adopted. In the metropolis movement of PM chain, a four-bond movement model is used. The average energy and average Helmholtz free energy with various elongation ratios λ are calculated by Monte Carlo simulation method. The average energy increases with elongation ratio λ and the average Helmholtz free energy decreases with elongation ratio λ. The elastic force f and the energy contribution to elastic force f_u can be obtained from f=∂〈A〉/∂r and f=∂〈U〉/∂r. We find that the elastic force f increases with elongation ratio λ and the energy contribution f_u decreases with elongation ratio λ, and f_u is less than zero. The ratio f_u/f is close to −0.21 for λ?1.25, and −0.04 to −0.35 for λ>1.25 at T=364 K. In our calculation, the rubber elasticity may be discussed in terms of the chemical structure of polymer chains.     

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.     

Elastic behavior of uniform star polymer chains

Elastic behaviors of uniform star polymer chains with two to seven branches (namely, functionality f = 2-7) are investigated using Monte Carlo simulation and the bond fluctuation model. Here chain dimensions and thermodynamic properties of uniform star polymer chains during the process of tensile elongation are studied, and comparisons with linear chain are also made. Static properties of chains such as chain sizes and asphericities of chains are calculated, and g-value of g = 〈S²〉_star/〈S²〉_linear decreases with elongation ratio increasing for different functionality f. Thermodynamic properties such as average energy 〈U〉, free energy per bond 〈A′〉 and elastic force F are also investigated during the process of tensile elongation. In the meantime, scatting functions P(q) are calculated for star polymer chains with different functionality f. Additionally, we also discuss the influence of elongation ratio on scattering form factor. The impenetrability of the star cores is known to cause a discontinuity in the osmotic pressure showed through a peak in the scattering functions, and some different behaviors in the tensile process for uniform star chain are obtained.     

A molecular study on the reinforcement of polymethylene elastomers

Monte Carlo simulations are carried out on filled networks of polymethylene (PM), which are modeled as composites of PM chains and three-dimensional cubic lattices of filler particles. Calculations are carried out for PM chains with various chain lengths n and various cubic unit dimensions a. The elastic behavior is investigated by using a realistic rotational-isomeric-state (RIS) model and enumeration calculation method. The average conformations, such as a priori probability P_η and the segmental orientation function 〈P₂(cosζ)〉 of PM chains are also calculated. In the process of tensile deformation, the a priori probability P_t increases with elongation ratio λ, however, it decreases with increasing cubic unit dimensions a. The segmental orientation distribution function 〈P₂(cosζ)〉 of deformed PM chains decreases with increasing cubic unit dimensions a, especially in the region of large deformation. Average Helmholtz free energy per bond becomes small when increasing cubic unit dimensions a, and average energy per bond becomes large when increasing cubic unit dimensions a. We find that the elastic force increases with elongation ratio for small λ, and abruptly for large λ. In the meantime, the energy contribution to elastic force is negative and significant. It is also shown that the elastic force and the energy contribution to elastic force is almost the same with various cubic unit dimensions a. The ratio f_u/f ranges from −0.4 to −0.6 at T=425 K. The reinforcement effects on the Helmholtz free energy 〈A〉 and energy 〈U〉 are important; however, the effect on the elastic force is insignificant. Our calculation may provide some insight into the macroscopic phenomena of rubber elasticity.     

Elastic behavior of bimodal poly(dimethylsiloxane) networks

The rubberlike elastic behavior of bimodal poly(dimethylsiloxane) (PDMS) networks was investigated by the Monte Carlo simulation method and enumeration calculation method on the basis of the rotational‐isomeric‐state (RIS) model. These bimodal PDMS networks consist of short chains (chain length from 10 to 20) as well as long chains (chain length equal to 150). For long PDMS chains, through generating many PDMS conformations in the equilibrium state using the Monte Carlo simulation method we can obtain the average Helmholtz free energy and the average energy. For short PDMS chains with chain lengths from 10 to 20, as the total number of conformations is only from 6.56 × 10³ to 3.87 × 10⁸, we adopt the enumeration calculation method. The deformation is partitioned nonaffinely between the long and short chains, and this partitioning can be determined by requiring the free energy of the deformed network to be minimized. Chain dimensions and thermodynamic statistical properties of bimodal PDMS networks at various elongation ratios are discussed. We find that elastic force f increases with elongation ratio λ; the energy contribution f_u to elastic force is significant, and the ratio of ranges from 0.15 to 0.36 at T = 343 K. In the meantime, elastic force f increases with the average energy 〈U〉. The energy change in the process of tensile elongation is taken over, which has been ignored in previous theories. Our calculations may provide some insights into the phenomena of rubberlike elasticity of bimodal networks. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 105–114, 2002     

Rigid rod anchored to infinite membrane

We investigate the shape deformation of an infinite membrane anchored by a rigid rod. The density profile of the rod is calculated by the self-consistent-field theory and the shape of the membrane is predicted by the Helfrich membrane elasticity theory [W. Helfrich, Z. Naturforsch. 28c, 693 (1973)]. It is found that the membrane bends away from the rigid rod when the interaction between the rod and the membrane is repulsive or weakly attractive (adsorption). However, the pulled height of the membrane at first increases and then decreases with the increase of the adsorption strength. Compared to a Gaussian chain with the same length, the rigid rod covers much larger area of the membrane, whereas exerts less local entropic pressure on the membrane. An evident gap is found between the membrane and the rigid rod because the membrane's curvature has to be continuous. These behaviors are compared with that of the flexible-polymer-anchored membranes studied by previous Monte Carlo simulations and theoretical analysis. It is straightforward to extend this method to more complicated and real biological systems, such as infinite membrane/multiple chains, protein inclusion, or systems with phase separation.     

Relation between Energy Contribution to Elastic Force and Strain Dependence of Modulus for Polybutadiene Vulcanizates

It is well known that the modulus G = r/(λ - λ^?2) varies with deformation, thus deviating from the predictions of statistical theories of rubber elasticity which require it to be constant. It has also been found that there is a nonnegligible energy contribution to the elastic force. It is postulated that these two phenomena are related because both arise from energetic interaction between chains.

Based on the lateral order of chains indicated by x-ray fiber diagrams of elongated noncrystallizable elastomers, it is suggested that energetic interaction of chains is induced by strain orientation. Proportionality between these two is assumed. The orientation distribution functions of end-to-end vectors and of statistical chain segments are considered. The proportionality constants are determined from the energy contribution to the strain dependence of the coefficient of thermal expansion. With the aid of these constants the modulus, corrected for energy contribution, is calculated. The observed and calculated elongation dependence of G agree reasonably well.

It is concluded that an energy interaction between aligned chains can account for the deviation of the observed stress elongation relation from the predictions of entropy elasticity theories.     

Elastic behavior of ring polymer chains

In this article, the conformational properties and elastic behaviors of ring polymers in the process of tensile elongation are investigated with the Monte Carlo method and the bond fluctuation model. The ratio of the mean‐square diameter <d²> to the mean‐square radius of gyration <S²> increases with the elongation ratio, λ, and the instantaneous shape of ring polymers is more symmetric than that of linear chains in the process of tensile elongation. Here <d²> for ring polymers rather than the mean‐square end‐to‐end distance <R²> for linear polymers is defined as the average of squared distances between two segments separated by N/2 bonds, where N represents the total number of bonds. Local quantities, that is, the mean‐square bond length <b²> and the mean bond angle <θ> increase with λ, especially for short ring chains. The <d²> and <S²> have the same relationship with the chain length, N, that is, <d²> ～ N^1.130±0.020 and <S²> ～ N^1.160±0.013 for a different λ. Some thermodynamics properties are also addressed here. The average energy per bond <U> decreases with λ and the average Helmholtz free energy and elastic force f increase with λ, especially for short ring chains. Comparisons with linear chains are also made. These investigations may provide insight into the elastic behaviors of ring polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 223–232, 2005     

Translocation of a proteinlike chain through a finite channel

We use the pruned-enriched-Rosenbluth method and the modified orientation-dependent monomer-monomer interaction model to study the translocation of a proteinlike chain through a finite channel. The mean-square radius of gyration per bond /N and shape factor of proteinlike chains with different secondary structures transporting through a finite channel with different channel radii R=1, 2, 3, 4, and 20 are investigated in the translocation. The average Helmholtz free energy per bond A/N and the mechanical force f are also presented. A/N remains unchanged when X(0)<0 and X(0)>1, and decreases monotonously when 0.5/N is also calculated in the process of translocation. An energy barrier is shown. The proteinlike chains must cross this energy barrier when they escape from the channel. The position of the maximum of /N depends on the secondary structures and the channel radius. We also discuss the average contact energy per bond c/N, the average alpha-helical energy per bond h/N, and the average beta-sheet energy per bond b/N.     

Energy landscapes for adsorption of a protein-like HP chain as a function of native-state stability

Dynamic Monte Carlo (DMC) simulations of the adsorption of simple protein-like chains are used to more clearly define the molecular basis for the dependence of adsorption thermodynamics on the stability of the unique lowest-energy "native state" conformation of the chain. Arai and Norde were among the first to show that proteins of low native-state stability strongly denature upon adsorption to weakly attractive sorbent surfaces, while relatively modest changes in conformation are observed in stable proteins under identical adsorption conditions. When the protein has a low native-state stability, favorable adsorption entropies are typically observed in such systems, leading to the general belief that the chain gains conformational entropy during adsorption through a net reduction in intramolecular interactions specific to the native-state structure. Analysis of energy landscapes generated from our DMC simulation results show that a net loss in specific intramolecular interactions can lead to a positive delta(ads)S under certain adsorption conditions. However, the influence of chain conformation on delta(ads)S is found to correlate more directly with the manner in which the unique states of the system are distributed among the energy levels available to the adsorbed chain. Delta(ads)S is found to tend toward a maximum for adsorption processes described by thermally averaged energy landscapes in which the energy levels carrying the highest Boltzmann weights have a high degree of conformational degeneracy. This condition is met when the average interaction energy between the chain and the sorbent equals that between two hydrophobic segments of the chain.