Kazumi Suematsu
In the gelation theory it has been implicitly assumed that (I) a cyclic bond is a finite bond that returns to itself; (II) cyclic bonds distribute at random in network structures. In this paper these two assumptions are reexamined from a new point of view. The physical soundness of the assumptions is assessed through comparison with experimental observations.
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Nano-pore based characterization of branched polymers
我们提出了一种新的表征方法的基础上的几何性质的限制空间中的无规支化聚合物。中心思想是，无规支化聚合物表现出作为通道尺寸的函数的穿过/堵塞纳米通道的过渡。该临界通道尺寸取决于支化程度，从而允许提取分子的支化信息。
The excluded volume effects of randomly branched polymers are investigated. To approach this problem we assume the Gaussian distribution of segments around the center of gravity. Once this approximation is introduced, we can make use of the same method as employed for linear molecules. By simulating a model-polymer system, it is found that the excluded volume effects of branched polymers are manifested pronouncedly under any conditions from the dilution limit to the melt, including the $Θ$ state; every result satisfies the restraining condition: $\langle s^2\rangle^{1/2} \ge N^{1/d}$ in accord…
We determine the distribution of free ends and the monomer insertion potential in the strongly-stretched limit for regularly and statistically branched polymer brushes. We find that the end density flattens in the limit of very strong branching with a concomitant enhancement of the grafting surface end density. This enhancement ensures for a wide range of parameters that a parabolic potential profile is preserved, even for large positive curvature of the brush surface. This considerably simplifies the analysis of copolymer phases.
Flow-injection of branched polymers inside nanopores
柔性链（线性或分支）可以通过使用流体动力学流动被迫进入狭窄的毛细管。在这里，我们通过考虑抽吸过程的渐进性质来纠正我们先前对这个问题的描述。我们发现，渗透的临界电流，$J\_c$，是由一个单一的斑点的毛细管大小的入口控制，其标度结构是相同的支链和直链。
We investigate the excluded volume effects in good solvents for the isolated comb polymers having $ν_{0}=1/4$. In particular, we investigate the change of the size exponent, $ν$, defined by $\langle s_{N}^{2}\rangle\propto N^{2ν}$, for the various fully-expanded configurations. The results show that, given the fully stretched backbone and side chains, the exponent takes the value, $ν=1/2$, irrespective of the configurational isomerization of side chains; only the pre-exponential factor changes.
Branched polymers can be classified into two categories that obey the different formulae: \begin{equation} ν= \begin{cases} \hspace{1mm}\displaystyle\frac{2(1+ν_{0})}{d+2} & \hspace{3mm}\mbox{for polymers with}\hspace{2mm}\displaystyleν_{0}\ge\frac{1}{d+1}\hspace{10mm}\text{(I)}\\[3mm] \hspace{5mm}2ν_{0}& \hspace{3mm}\mbox{for polymers with}\hspace{2mm}\displaystyleν_{0}\le\frac{1}{d+1}\hspace{10mm}\text{(II)} \end{cases}\notag \end{equation} for the dilution limit in good solvents. The category II covers the exceptional polymers having fully expanded configurations. On the basis of these equa…
The viscosity enhancement of a solvent produced by the addition of thickening branched polymers is predicted as a function of polymer concentration, branch length and persistence length, and strength of the covalent bonding interactions. Non equilibrium, stationary state Poiseuille numerical simulations are performed using the dissipative particle dynamics model to obtain the viscosity of the fluid. It is found that the clustering of the polymers into aggregates raises the viscosity and that it is more strongly affected by the strength of the bonding interactions. General scaling relationships…
Conformational Transition of H-shaped Branched Polymers
采用动态蒙特卡罗模拟方法，模拟了不同主链（主链）和侧链（支链）长度的H型支化聚合物的构象转变。H型聚合物与等效线性聚合物相比，表现出θ温度的降低，伴随着更小的链尺寸。我们观察到支链对骨架尺寸的影响比相反的影响更明显，这归因于分子内普遍存在的构象异质性。随着分枝长度的增加，主链以卷曲和球状状态略微伸展。然而，在崩溃前（cf。皱球）状态下，主链尺寸随分支长度的增加而减小。我们将这种非单调行为归因于在塌缩转变过程中排斥体积相互作用和链内珠-珠吸引相互作用之间的相互作用。结构分析表明，固有的构象异质性促进了具有分离的主链和分支单元的塌陷结构（类似于“三明治”或“Janus”形态）的形成，而不是由所有单元组成的均匀分布的结构。随着主干或分支长度的增加，塌陷小球的形状变得更加球形。
Branched Polymers and Percolation
我们研究了支化聚合物的一个假定模型，该模型在二维上被证明是普通渗流的普适类。我们证实了这一点，高统计模拟，并表明，它是在渗透普适性类也为三个维度，与以前的索赔。这些先前的研究似乎被这个模型中的缩放的巨大修正所误导。
Axial dispersion in dilute solutions of linear and branched polymers in parallel-plate and expansion-contraction microchannels
利用多粒子碰撞动力学模拟，研究了线性、梳形和星形聚合物在平行板和正弦膨胀-收缩微通道中的轴向分散，发现分散系数依赖于聚合物构型和浓度，并通过考虑聚合物扩散系数的限制效应和流场贡献，使用考虑非均匀分布的理论合理预测了平行板微通道中的分散系数。
The confinement free energies of non-ideal branched polymers and ideal unbranched polymers are the same
我们使用降维的方法表明，排除体积相互作用限制在两个平板之间的支化聚合物，在热力学极限，限制自由能和密度分布是相同的理想的线性聚合物具有相同数量的单体和相同的单体板相互作用潜力。由于支化引起的冷凝被由于排除的体积相互作用引起的溶胀精确地补偿。
The contributed paper by Naserifar and Goddard reports that their RexPoN water model under ambient conditions simulates liquid water as a dynamic polydisperse branched polymer, which they speculate explains the existence of the liquid-liquid critical point (LLCP) in the supercooled region. Our work addresses several serious factual errors and needless speculation in their paper about their interpretation of their model and its implication for the LLCP in supercooled water.
The behavior of annealed branched polymers near adsorbing surfaces plays a fundamental role in many biological and industrial processes. Most importantly single stranded RNA in solution tends to fold up and self-bind to form a highly branched structure. Using a mean field theory, we both perturbatively and numerically examine the adsorption of branched polymers on surfaces of several different geometries in a good solvent. Independent of the geometry of the wall, we observe that as branching density increases, surface tension decreases. However, we find a coupling between the branching density…
Crosslinked polymer chains with excluded volume: A new class of branched polymers?
在本说明中，考虑了具有和不具有排除体积相互作用的微凝胶。基于早期的精确计算高斯微凝胶，这是由自交联（与$M$交联）的聚合物链的链长$N$弗洛里型近似形成的，以获得第一次洞察他们在溶液中的行为。结果表明，存在两种不同类型的微凝胶：一种特殊类型的支化聚合物，其尺寸尺度为$R \propto N^{2/5} M^{-1/5}$，而不是$R \propto N^{1/2}$。第二种类型是$c^*$ -微凝胶，其平均筛目尺寸$r$是溶胀的，并形成具有$r = a (N/M)^{3/5}$形式的标度律的自回避行走。
Statistics of randomly branched polymers in a semi-space
本文研究了无规支化的3-官能$N$ -链聚合物链的统计性质，该链的一个点固定在三维空间中距离不可穿透表面$d$的位置上，不含排斥体积.精确求解Dyson型方程的三维配分函数$Z(N,d)=N^{-θ} e^{γN}$，我们发现“表面”的临界指数$θ={5/2}$，以及密度分布的3-功能单元和死端。我们的方法还可以计算三维半空间中无规支化聚合物的成对关联函数。
Branched-polymer to inflated transition of self-avoiding fluid surfaces
利用蒙特卡罗模拟技术研究了动态三角网格上自回避流体表面模型的相变。我们报告的支化聚合物和膨胀相之间的连续过渡在${\it Δ}p \!=\!0$，其中${\it Δ}p (=\!p_{\rm in}\!-\!p_{\rm out})$是内外侧的表面之间的压力差。该转变的特征在于封闭体积相对于弯曲刚度$κ$和压力差${\it Δ}p$的变化的几乎不连续的变化。没有表面波动过渡伴随着这种过渡到具有顶点数量的表面$N\!=\!2562$。
Disorder effects on the static scattering function of star branched polymers
我们提出了一个分析的影响f-臂星形支化聚合物在d维的静态散射函数的结构无序。为此，我们考虑模型的星形聚合物沉浸在一个良好的溶剂中的结构缺陷的存在下，相关的大距离r根据幂律\sim r^{-a}。特别地，我们感兴趣的是相同分子量的星形和线性聚合物的回转半径的比率g（f），这是一个通用的实验可测量的量。我们应用一个直接的聚合物重整化方法，并在双\varepsilon =4-d，δ=4-a-展开内评估结果。我们发现g（f）随着δ的增加而增加。因此，无序相关性的增加导致相对于相同分子量的线性聚合物的星的尺寸测量的增加。
Renormalized field theory of collapsing directed randomly branched polymers
我们提出了一个动力学场论的定向随机支化聚合物，特别是他们的崩溃过渡。我们开发了一个唯象模型的形式，一个随机响应功能，使我们能够解决几个有趣的问题，如膨胀相和崩溃过渡的缩放行为。对于膨胀相，我们发现，通过选择适当的模型参数，我们的随机泛函减少到一个描述的弛豫动力学附近的杨-李奇异边缘。这证实了溶胀支化聚合物的标度行为受杨-李普适类的控制，这是很久以前就知道的。我们的论文的主要焦点在于定向支化聚合物的塌缩转变。我们证明了任意阶的重正化微扰理论与$\varepsilon$ -展开，这种过渡属于相同的普适类定向渗流。
Bottle brushes are polymeric macromolecules made of a linear polymeric backbone grafted with side chains. The choice of the grafting density σg, the length ns the grafted side chains and their chemical nature fully determines the properties of each macromolecule, such as its elasticity and its folding behaviour. Typically, experimental bottle brushes are systems made of tens of thousands of monomeric units, rendering a computational approach extremely expensive, especially in the case of bottle brush solutions. A proper coarse graining description of these macromolecules thus appears essential…
Scaling exponents for a monkey on a tree - fractal dimensions of randomly branched polymers
我们利用重整化动力学场论研究了大尺寸无规支化聚合物上扩散和其他输运过程（包括自回避行走和导电）的渐近性质。我们专注于溶胀相和塌陷过渡，在聚合物中的循环是无关紧要的。在这里，聚合物的渐近统计是格树的渐近统计，在它们上面的扩散让人想起猴子爬上树。我们计算一组通用的标度指数，包括扩散指数和分形维数的最小路径2-循环顺序，并在可用的情况下，将它们与数值结果进行比较。
Branched Polymers on the Given-Mandelbrot family of fractals
本文用精确实空间重整化方法研究了Given-Mandelbrot分形族上n个键的支化聚合物的不同构型数的平均每格点数A_n。该族的不同成员由整数参数b表征，b > 1。当b从2变化到无穷大时，分形维数从$ log_{_2} 3$变化到2。我们发现对于所有b > 2，A_n随$ λ^n exp(b n ^ψ)$变化，其中$λ$和$b$是常数，而$ 0 < ψ<1$是常数.我们确定的指数$ψ$，和尺寸指数$ν$（聚合物的平均直径变化为$n^ν$），完全为所有b > 2。这推广了Knezevic和Vannimenus对b = 3的早期结果[Phys. Rev { \bf B 35}（1987）4988]。
Fresh look at randomly branched polymers
我们开发了一个新的，各向同性的随机支化聚合物的动力学场论，我们使用这个模型与重整化群（RG）研究这些聚合物的物理中的几个突出的问题。我们的模型提供了一个替代的有利位置，通过降维理解溶胀相。我们揭示了一个隐藏的Becchi-Rouet-Stora（BRS）对称性的模型，描述了崩溃（$θ$ -）过渡到紧凑的聚合物构象，并计算临界指数为2-循环顺序。事实证明，这些指数的长期1-循环结果并不完全正确。RG流的失控表明，所谓的$θ^\prime$ -转变可能是波动诱导的一级转变。
Mathematical expressions for mass distributions around the center of gravity are derived for branched polymers with the help of the Isihara formula. We introduce the Gaussian approximation for the end-to-end vector, $\vec{r}_{Gν_{i}}$, from the center of gravity to the $i$th mass point on the $ν$th arm. Then, for star polymers, the result is \begin{equation} φ_{star}(s)=\frac{1}{N}\sum_{ν=1}^{f}\sum_{i=1}^{N_ν}\left(\frac{d}{2π\left\langle r_{Gν_{i}}^{2}\right\rangle}\right)^{d/2}\exp\left(-\frac{d}{2\left\langle r_{Gν_{i}}^{2}\right\rangle}s^{2}\right)\notag \end{equation} for a sufficiently …
Numerical values of lattice star entropic exponents $γ_f$, and star vertex exponents $σ_f$, are estimated using parallel implementations of the PERM and Wang-Landau algorithms. Our results show that the numerical estimates of the vertex exponents deviate from predictions of the $ε$-expansion and confirms and improves on estimates in the literature. We also estimate the entropic exponents $γ_\mathcal{G}$ of a few acyclic branched lattice networks with comb and brush connectivities. In particular, we confirm within numerical accuracy the scaling relation $$ γ_{\mathcal{G}}-1 = \sum_{f\geq 1} m_f…
The collapse transition of randomly branched polymers -renormalized field theory
本文提出了一个随机支化各向同性聚合物的最小动力学模型，并在重整化场论的框架下研究了该模型。对于溶胀相，我们表明，我们的模型提供了一条路线，从不同的角度来理解既定的降维结果。对于塌陷$θ$过渡，我们发现了一个隐藏的贝基-Rouet-Stora超对称，信号树配置的唯一相关性。我们纠正了长期存在的1-循环结果的临界指数，我们把这些结果的2-循环顺序。对于坍缩的$θ^{\prime}$ -跃迁，我们发现了一个重整化群流的逃逸，这使得我们相信这个跃迁是涨落诱导的一级跃迁。我们的动力学模型使我们能够计算的最短路径上的随机支化聚合物在溶胀相的分形维数，以及在崩溃过渡和相关的分形维数。
We briefly review the recent advances in the rheology of entangled polymers and identify emerging research trends and outstanding challenges, especially with respect to branched polymers. Emphasis is placed on the role of well-characterized model systems, as well as the synergy of synthesis-characterization, rheometry and modeling/simulations. The theoretical framework for understanding the observed linear and nonlinear rheological phenomena is the tube model which is critically assessed in view of its successes and shortcomings, whereas alternative approaches are briefly discussed. Finally, i…
We discuss the extension of the empirical equation: $\left\langle s_{N}^{2}\right\rangle_{0}\propto g\,l^{2}$, where the subscript 0 denotes the ideal value with no excluded volume and $g$ the generation number from the root to the youngest (outermost) generation. By analogy with the linear chain problem, we introduce the assumption that the scaling relation, $\left\langle s_{N}^{2}\right\rangle_{0}\propto g^{2λ}\,l^{2}$, exists for arbitrary polymeric architectures, where $λ$ is an exponent for the backbone structure. Then, making use of the relationship between $g$ and $N$ (monomer number), …
Viral RNA as a branched polymer
本章探讨如何通过平面图将病毒长 RNA 分子视为支化聚合物，揭示其特征性紧凑度，并展示如何结合聚合物物理学已知结果与额外相互作用来扩展该模型。
Delayed Arm Retraction Controls the Nonlinear Oscillatory Response of Long-Chain-Branched Polymer Melts
研究长链支化聚合物熔体非线性振荡响应，提出分子管理论，纳入分支点力传递和延迟臂回缩，解释NLI特征最大值，预测不同非线性区域及相关参数，为非线性傅里叶流变学提供分子解释并联系聚合物结构。
Universal properties of branched copolymers in dilute solutions
本文通过解析重整化与晶格模拟相结合的方法，系统研究了花环型和哑铃形支化共聚物在稀溶液中的普适构象性质，定量揭示了组分间相互作用对尺寸特征的影响。
Star polymer undergoes a transformation from a group of loosely coupled chains at low number of arms to a dense hairy colloid at their high number. This change affects solubility, aggregation and rheological behavior and is of much practical interest. We study the range of size and shape properties of the star molecule and of its individual arms upon this transformation. Theoretical calculations are based on a continuous chain model and are performed in the first order in $ε=4-d$. Computer simulations are done by the dissipative particle dynamics and in part by Monte Carlo method and the resul…
We analyze the statistics of loops formation in $f$-branched star polymers in an environment with structural defects, correlated at large distances $r$ according to a power law $\sim r^{-a}$. Applying the direct polymer renormalization approach, we found the values of the set of universal exponents, governing the scaling of probabilities of various types of loops in macromolecules.
Unlike hard materials such as metals and ceramics, rubbery materials can endure large deformations due to the large conformational degree of freedom of the crosslinked three-dimensional polymer network. However, the effect of the branching factor of the network on the ultimate mechanical properties of rubbery materials has not yet been clarified. This study shows that tri-branching, which entails the lowest branching factor, results in a large elastic deformation near the theoretical upper bound. This ideal elastic limit is realized by reversible strain-induced crystallization, providing on-de…
Effects of Molecular Composition and Chain Length on the Interfacial and Thermodynamic Properties of Cyclic and Linear Polymer Blends
本研究利用Kremer-Grest模型探讨分子量和链架构对环状与线形聚合物共混物界面吸附及热力学性质的影响，旨在为可持续材料设计提供见解。
A mean field rate theory description of the homo- and co-polymerization of $f$-functional molecules is developed, which contains the formation of short cyclic structures inside the network. The predictions of this model are compared with Monte-Carlo simulations of cross-linking of star polymers in solution. We find that homo-polymerizations are well captured by mean-field models at concentrations larger than one quarter of the geometrical overlap concentration. All simulation data can be fit using a single geometric parameter for cyclization. The simulation data reveal that within the range of…
Self-diffusion in binary blends of cyclic and linear polymers
一个晶格模型被用来估计缠结的环状和线性聚合物的自扩散在不同的组成的共混物。为了解释模拟结果，我们提出了一个极小模型的基础上的物理思想，渗透线性链施加在环状聚合物上的约束必须被释放，才可以扩散超过一个回转半径。模拟和最近报道的关于缠结DNA溶液的实验数据都支持在广泛的混合物组成、浓度和分子量范围内的简单模型。
Influence of chain topology and bond potential on the glass transition of polymer chains simulated with the bond fluctuation model
本文将键涨落模型应用于线性链和具有规则小支链的链的玻璃化转变的研究。冷却和随后的加热曲线获得的链能量，也为珠跳的平均接受概率。为了模拟玻璃化的不同趋势，引入了一个因子B，该因子B测量了键合电位相对于长程电位（即间接键合珠之间的分子内或分子间电位）的强度。（B值越高，导致对最高键长和更高总能量的偏好，这意味着更大的玻璃化倾向。对于直链，考虑了不同的情况：无长程势、无键势和B的几种选择。此外，我们考虑了线性链中交替键的两个不同的B值。在支链的情况下，也研究了主链和支链中具有不同B值的分子。可能存在的结晶已被其特征在于通过计算集体光散射功能的不同样品退火后，在一个方便的温度低于开始结晶。得出的结论是，在具有支链的系统中，结晶更有效地遗传，并且对于较高的B值也是如此。在主链键中具有最高B值的支化分子在加热曲线中表现出两个不同的转变，这可能与两个玻璃化转变有关。这种行为已经在实验中检测到的链具有相对较长的柔性分支。
Cyclic motion and inversion of surface flow direction in a dense polymer brush under shear
使用分子模拟，我们研究了一个聚合物刷在与一个明确的溶剂下Couette和Poietille流的性质。溶剂由化学上相同的链组成。我们提出的证据表明，个人，未纠缠的链在密集的刷表现出循环，翻滚运动和非高斯波动的分子取向类似的行为，孤立的拴系链在剪切流。集体分子运动引起的流体动力学流动方向在刷涂表面附近的反转。利用Couette和Poiffille流，我们调查到什么程度的刷涂表面的效果可以描述的Navier滑移条件。
Self-healing polymers crosslinked by solely reversible bonds are intrinsically weaker than common covalently crosslinked networks. Introducing covalent crosslinks into a reversible network would improve mechanical strength. It is challenging, however, to apply this design concept to dry elastomers, largely because reversible crosslinks such as hydrogen bonds are often polar motifs, whereas covalent crosslinks are non-polar motifs, and these two types of bonds are intrinsically immiscible without co-solvents. Here we design and fabricate a hybrid polymer network by crosslinking randomly branche…
A Topology-Preserving Python Framework for Reliable Initialization of Star and Cyclic Polymer Architectures in Molecular Dynamics (LAMMPS) Simulations
提出一种保持拓扑结构的Python框架，通过确定性键连接、精确环闭合、排除体积和空间哈希重叠检测，生成LAMMPS兼容的星形和环形聚合物初始构型，显著减少重叠引起的数值不稳定并提高模拟可靠性。
Concatenation and equilibrium swelling of Olympic gels, which are composed of entangled cyclic polymers, is studied by Monte Carlo Simulations. The average number of concatenated molecules per cyclic polymers, $f_n$, is found to depend on the degree of polymerization, $N$, and polymer volume fraction at network preparation, $ϕ_0$, as $f_n ~ ϕ_0^{ν/(3ν-1)}N$ with scaling exponent $ν = 0.588$. In contrast to chemically cross-linked polymer networks, we observe that Olympic gels made of longer cyclic chains exhibit a smaller equilibrium swelling degree, $Q ~ N^{-0.28} ϕ_0^{-0.72}$, at the same po…
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