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Kazumi Suematsu

Publications and source records attributed to Kazumi Suematsu.

At least 19 recordsLinked to original sources
arXiv2026

On the Determination of Gel Points

A critical composition of cross-linked polysiloxanes observed by Scanlan and Winter is reinvestigated in comparison with the theory of gelation. We assume, based on the Scott findings, the geometric distribution for one of the monomers, divinyl-terminated poly(dimethylsiloxane). Calculation results show that the two theories are in near-consistency, supporting the Scanlan-Winter estimation based on the linear viscoelastic theory. On the other hand, there is a disturbing result that calculation using the mean molecular weight, $M_{n}$, leads to exact agreement between the two theories, suggesting that the distribution is in effect monodisperse, contrary to the assumed geometric one and also the observed polydispersity, $M_w/M_n=2.1$. Further experimental studies employing monodisperse monomers would be highly valuable to consolidate the bridge between these two fundamental theories.

cond-mat.soft↗
arXiv2024

Critical Nature of the Size Exponent of Polymers

On the basis of the thermodynamic theory of the excluded volume effects, we show that the size exponent varies abruptly, depending on the change of the segment concentration. For linear polymers, the exponent changes discontinuously from $ν=3/5$ for the isolated system ($\barϕ=0$) in good solvents to $ν=1/2$ in the finite concentration ($0<\barϕ\le1$), while for branched polymers having $ν_{0}=1/4$, the corresponding exponent varies from $ν=1/2$ ($\barϕ=0$) to $ν\cong 1/3$ ($0<\barϕ\le1$).

cond-mat.soft↗
arXiv2022

Size Exponents of Branched Polymers/ Extension of the Isaacson-Lubensky Formula and the Application to Lattice Trees

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 equalities, we discuss the size exponents of the nested architectures and the lattice trees. In particular, we compare our preceding result, $ν_{d=2}=1/2$, for the $z$=2 polymer having $ν_{0}=1/4$ with the numerical result, $ν_{d=2}\doteq 0.64115$, for the lattice trees generated on the 2-dimensional lattice. Our conjecture is that while both the conclusions in polymer physics and condensed matter physics are correct, the discrepancy arises from the fact that the lattice trees are constructed from less branched architectures than the branched polymers having $ν_{0} = 1/4$ in polymer physics. The present analysis suggests that the 2-dimensional lattice trees are the mixture of isomers having the mean ideal size exponent of $\barν_{0}\doteq0.32$.

cond-mat.soft↗
arXiv2022

Branched Polymers with Excluded Volume Effects/ Configurations of Comb Polymers in Two- and Three-dimensions

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.

cond-mat.soft↗
arXiv2021

Branched Polymers with Excluded Volume Effects/ Relationship between Polymer Dimensions and Generation Number

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), we can deduce the exponent, $ν$, for polymers with various architectures. The theory of the excluded volume effects impose the severe restriction on the quantities: $ν_{0}$, $ν$, and $λ$; for instance, the inequality, $ν_{0}\ge\frac{1}{d+1}$, must be satisfied for isolated polymers in good solvents. An intriguing question is whether or not there exists an actual molecule that violates this inequality. We take up two examples having $ν_{0}=1/4$ for $d=2$ and $ν_{0}=1/6$ for $d=3$, and discuss this question.

cond-mat.soft↗
arXiv2020

Segment Distribution around the Center of Gravity of a Triangular Polymer

The segment distribution around the center of gravity is investigated for a special comb polymer (triangular polymer) having the side chains of the same generation number, $g$, as the main backbone. Common to all the other polymers, the radial mass distribution is expressed as the sum of the distribution functions for the end-to-end vectors, $\{\vec{r}_{Gh}\}$, from the center of gravity to the monomers on the $h$th generation; the result being, for a large $g$, \begin{equation} φ_{\text{triang}}(s)=\frac{1}{N}\left\{\sum_{h=1}^{g}\left(\frac{d}{2π\left\langle r_{Gh}^{2}\right\rangle}\right)^{\frac{d}{2}}\text{Exp}\left(-\frac{d}{2\left\langle r_{Gh}^{2}\right\rangle}s^2\right)+\sum_{h=2}^{g}\sum_{j=1}^{g-h}\left(\frac{d}{2π\left\langle r_{Gh_{j}}^{2}\right\rangle}\right)^{\frac{d}{2}}\text{Exp}\left(-\frac{d}{2\left\langle r_{Gh_{j}}^{2}\right\rangle}s^2\right)\right\}\notag \end{equation} It is found that the mean square of the radius of gyration varies as $\left\langle s_{N}^{2}\right\rangle_{0}\doteq\frac{7}{15}\,g\,l^{2}$, as $g\rightarrow\infty$. Since $g\propto \sqrt{N}$ for the triangular polymer, this leads to $\left\langle s_{N}^{2}\right\rangle_{0}^{1/2}\propto N^{1/4}$, giving the same exponent as observed for the randomly branched polymer. On the basis of the present result, we put forth that all the known polymers obey the equality: $\left\langle s_{N}^{2}\right\rangle_{0}=A\, g\,l^{2}$, where $A$ is a polymer-species-dependent coefficient and also depends on the choice of the root monomer. We discuss the extension of this empirical equation.

cond-mat.soft↗
arXiv2020

Segment Distribution around the Center of Gravity of Branched Polymers

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 large $N$, where $f$ denotes the number of arms. It is found that the resultant $φ_{star}(s)$ is, unfortunately, not Gaussian. For dendrimers \begin{equation} φ_{dend}(s)=\sum_{h=1}^{g}ω_{h}\left(\frac{d}{2pi\left\langle r_{G_{h}}^{2}\right\rangle}\right)^{d/2}\exp\left(-\frac{d}{2\left\langle r_{G_{h}}^{2}\right\rangle}s^{2}\right)\notag \end{equation} where $ω_{h}$ denotes the weight fraction of masses in the $h$th generation on a dendrimer constructed from $g$ generations, so that $\sum_{h=1}^{g}ω_{h}=1$. To be specific, $ω_{1}=1/N$ and $ω_{h}=(f-1)^{h-2}/N$ for $h\ge 2$. These distributions can be described by the same grand sum of each Gaussian function for the end-to-end distance from the center of gravity to each mass point. Note that for a large $f$ and $g$, the statistical weight of younger generations becomes dominant. As a consequence, the mass distribution of unperturbed dendrimers approaches the Gaussian form in the limit of a large $f$ and $g$. It is shown that the radii of gyration of dendrimers increase logarithmically with $N$, which leading to the exponent, $ν_{0}=0$. An example of randomly branched polymers is also discussed.

cond-mat.soft↗
arXiv2018

Alternative Approach to the Excluded Volume Problem The Critical Behavior of the Exponent $ν$

We present the alternative derivation of the excluded volume equation. The resulting equation is mathematically identical to the one proposed in the preceding paper. As a result, the theory reproduces well the observed points by SANS (small angle neutron scattering) experiments. The equation is applied to the coil-globule transition of branched molecules. It is found that in the entire region of poor solvent regimes ($T<Θ$), the exponent $κ=d\logα\,/\,d\log N\, (N\rightarrow\infty)$ takes the value $\frac{1}{12}$, showing that contrary to the case of linear molecules ($κ=-\frac{1}{6}$), the expansion factor increases indefinitely as $N$ increases. The theory is then applied to concentrated systems in good solvents. It is found that for the entire region of $0<\barϕ\le 1$, the gradients $κ$ seem to converge on a common value lying somewhere from $κ=\frac{1}{12}$ to $0.1$. Since $ν_{dilute}=\tfrac{1}{2}$, $ν_{melt}=\tfrac{1}{3}$, and $0.33\cdots\leν_{conc}\,(=ν_{0}+κ) <0.35$ for $0<\barϕ\le 1$, the simulation results suggest that the exponents $κ$ and $ν$ change abruptly from phases to phases; there are no intermediate values between them, for instance between $ν_{dilute}$ and $ν_{melt}$.

cond-mat.soft↗
arXiv2017

Volume Expansion of Branched Polymers

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 with our experiences. As a result the Gaussian approximation extracts the essential features of the excluded volume effects of branched molecules.

cond-mat.soft↗
arXiv2016

Excluded Volume Effects of Branched Molecules

The expansion factor, $α^{2}=\langle s_{N}^{2}\rangle/\langle s_{N}^{2}\rangle_{0}$, of branched molecules in the melt state is estimated. The equilibrium expansion factor is determined as the point in which all the inhomogeneity terms of the osmotic potential, $ΔG_{osmotic}$, go to zero. Numerical analysis shows that $\log\,α=0.082\,\log N+\text{const.}$ for $10^{3}\le N\le 10^{7}$, giving $α\cong \text{const.}\,N^{1/12}$ so that $\langle s_{N}^{2}\rangle^{1/2}\propto N^{1/3}$ which coincides with the value for the critical packing density.

cond-mat.soft↗
arXiv2015

Cyclic Bonds in Branched Polymers

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.

cond-mat.soft↗
arXiv2015

Gelation Paradox

The gelation paradox first raised by Stockmayer is re-examined by comparing the extent of reaction in sol phase and that in the interior of gel. It is shown that the Stockmayer limit, 2/f, for the extent of reaction is the lowest limit in gel phase, as well as being the highest limit for sol molecules.

cond-mat.soft↗
arXiv2014

Radius of Gyration of Randomly Branched Molecules

The mathematical derivation of the mean square radius of gyration, , of branched polymers is reinvestigated from a kinetic-equation-point of view. In particular we derive the corresponding quantity of the A-R-Bf-1 model; the result showing that the mean square radius of gyration is precisely identical with that of the R-Af model.

cond-mat.soft↗
arXiv2014

Molecular Weight Dependence of Excluded Volume Effects

Molecular weight dependence of excluded volume effects is examined. The swollen-to-unperturbed coil transition point shifts to lower concentration range with increasing molecular weight (Mw). It is shown that in the limit of the infinite molecular weight, the excluded volume effects should vanish in all concentration range, except for the only one point, Co = 0. Quite in contrast, for short chains, the excluded volume effects never disappear even at the melt state.

cond-mat.soft↗
arXiv2013

Concentration Invariance of Cyclic Species

Concentration invariance of cyclic species in the irreversible polymerization is examined. The simulation shows that the invariance theorem holds in good approximation for the irreversible process also. The physical soundness of the underlying simulation equations is confirmed through comparison with the recent experimental observations carried out by the Nagoya university group.

physics.chem-ph↗