Activation Enthalpies for Plastic Deformation

Chang-Hong Kim,Tai-Kyue Ree Korean Chemical Society 1980 Bulletin of the Korean Chemical Society Vol.1 No.1

Activation energies for plastic deformation calculated from traditional phenomenological equations have been criticized frequently since the values are different by authors, and also by experimental conditions. The reasons of different activation enthalpies are clarified in this study. Our method for calculating activation enthalpies based on the authors' theory of plastic deformation was presented and discussed. The method was applied to various cases of alloys, the calculated activation enthalpies are listed and compared with the activation energies obtained by the traditional methods in order to show the reasonableness of our method. The physical meaning of the activation enthalpies which we found was clarified.

Derivation of the WLF Equation from the Theory of Rate Process

이태규,전무식,Ree, Tai-Kyue,Jhon, Mu-Shik Korean Chemical Society 1970 대한화학회지 Vol.14 No.1

"Significant liquid structure"의 이론과 반응 속도 이론을 이용 WLF점도식 꼴을 도출하였다. 반 실험적 WLF 점도식 내 실험 Parameter와 도출된 이론식 중의 해당된 항을 비교 검토하였다. The WLF equation is derived from the theory of rate processes in conjunction with the theory of liquids of significant structures. The empirical parameters in the WLF equation are discussed and compared with the corresponding quantities in the derived equation.

Molecular Theory of Plastic Deformation (Ⅲ)$^*$

Kim, Jae-Hyun,Ree, Tai-Kyue,Kim, Chang-Hong Korean Chemical Society 1981 Bulletin of the Korean Chemical Society Vol.2 No.3

(1) The flow data of f (stress) and ${\dot{s}$ (strain rate) for Fe and Ti alloys were plotted in the form of f vs. -ln ${\dot{s}$ by using the literature values. (2) The plot showed two distinct patterns A and B; Pattern A is a straight line with a negative slope, and Pattern B is a curve of concave upward. (3) According to Kim and Ree's generalized theory of plastic deformation, pattern A & B belong to Case 1 and 2, respectively; in Case 1, only one kind of flow units acts in the deformation, and in Case 2, two kinds flow units act, and stress is expressed by $f={X_1f_1}+{X_2f_2}$where $f_1\;and\;f_2$ are the stresses acting on the flow units of kind 1 and 2, respectively, and $X_1,\;X_2$ are the fractions of the surface area occupied by the two kinds of flow units; $f_j=(1/{\alpha}_j) sinh^{-1}\;{\beta}_j{{\dot{s}}\;(j=1\;or\;2)$, where $1/{\alpha}_j\;and\;{\beta}_j$ are proportional to the shear modulus and relaxation time, respectively. (4) We found that grain-boundary flow units only act in the deformation of Fe and Ti alloys whereas dislocation flow units do not show any appreciable contribution. (5) The deformations of Fe and Ti alloys belong generally to pattern A (Case 1) and B (Case 2), respectively. (6) By applying the equations, f=$(1/{\alpha}_{g1}) sinh^-1({\beta}_{g1}{\dot{s}}$) and $f=(X_{g1}/{\alpha}_{g1})sinh^{-1}({\beta}_{g1}{\dot{s}})+ (X_{g2}/{\alpha}_{g2})\;shih^{-1}({\beta}_{g2}{\dot{s}})$ to the flow data of Fe and Ti alloys, the parametric values of $x_{gj}/{\alpha}_{gj}\;and\;{\beta}_{gs}(j=1\;or\;2)$ were determined, here the subscript g signifies a grain-boundary flow unit. (7) From the values of ($({\beta}_gj)^{-1}$) at different temperatures, the activation enthalpy ${\Delta}H_{gj}^{\neq}$ of deformation due to flow unit gj was determined, ($({\beta}_gj)^{-1}$) being proportional to .$k_{gj}$, the jumping frequency (the rate constant) of flow unit gj. The ${\Delta}H_{gj}\;^{\neq}$ agreed very well with ${\Delta}H_{gj}\;^{\neq}$ (self-diff) of the element j whose diffusion in the sample is a critical step for the deformation as proposed by Kim-Ree's theory (Refer to Tables 3 and 4). (8) The fact, ${\Delta}H_{gj}\;^{\neq}={\Delta}H_{j}\;^{\neq}$ (self-diff), justifies the Kim-Ree theory and their method for determining activation enthalpies for deformation. (9) A linear relation between ${\beta}^{-1}$ and carbon content [C] in hot-rolled steel was observed, i.e., In ${\beta}^{-1}$ = -50.2 [C] - 40.3. This equation explains very well the experimental facts observed with regard to the deformation of hot-rolled steel..

Chain Length Effect on the Configurational Properties of an n-Alkane Chain in Solution

Jeon, Seung-Ho,Ree, Tai-Kyue,Oh, In-Joon Korean Chemical Society 1986 Bulletin of the Korean Chemical Society Vol.7 No.5

Dynamic and equilibrium properties of n-alkane chains immersed in solvent molecules have been investigated by a molecular dynamics method. The n-alkane chain is assumed to be a chain of elements (CH$_2$) interconnected by bonds having a fixed bond length and bond angle, but each bond of the chain is allowed to execute hindered internal rotation. We studied the effect of the number of the chain elements (N$_c$ = 10, 15 and 20) on the equilibrium properties of the system, e.g., the pair correlation functions between a chain element and solvent molecules, g$_{cs}$(r), and between the chain elements, g$_{cc}$(r), and the configurational properties such as the mean-square end-to-end distance < R$^2$ >, the mean-square radius of gyration < S$^2$ >, and the eigenvalues of the moment-of-inertia tensor < S$_i^2$ > / < S$^2$ > (i = 1, 2 and 3). We also studied the dynamic properties of the system, e.g., the autocorrelation function C(A;t) where A = R$^2$(t), = S$^2$(t), or = ${\vec{V}}(t)({\vec{V}}$ = velocity of the center of mass), and the diffusion coefficient D. The g$_{cs}$(r)'s are almost equal irrespective of the change of Nc while g$_{cc}$(r) becomes larger as N$_c$ increases; The MD computed configurational properties < R$^2$2 > and < S$^2$ > were found to be a little different from the values calculated from the statistical equations of < R$^2$ > and < S$^2$ >, it may be due to the fact that our model for the MD simulations includes a long-range volume effect. From the < S$_i^2$ > / < S$^2$ >, it is found that the chain molecule has a nearly spherical shape irrespective of the variation of N$_c$. For the dynamic properties we found that the C(R$^2$;t) and C(S$^2$;t) of lower N$_c$ decay faster than those of higher N$_c$, while the C($\vec V$;t) of the center of mass in the chain is weakly dependent on the N$_c$. The center of mass diffusion coefficient D$_c$ decreases as N$_c$ increases while the end point diffusion coefficient D$_e$ is nearly equal irrespective of the change of N$_c$.

Temperature Effect on the Configurational Properties of an n-Decane Chain in Solution

Oh, In-Joon,Ree, Tai-Kyue Korean Chemical Society 1984 Bulletin of the Korean Chemical Society Vol.5 No.4

Equilibrium and dynamical behaviors of an n-alkane poymer (decane) in solution have been investigated by a molecuar dynamics simulation method. The polymer is assumed to be a chain of elements $(CH_2)$ interconnected by bonds having a fixed bond length and bond angle, but esch bond of the polymer is allowed to execute hindered internal rotation. The calculation explicitly considers the molecular naturer of solvent by including the intermolecular interactions between slovent-solvent molecules and chain element-solvent molecule. We present the results of calculations on (1) equilibrium properties (the solvent molecule-chain element pair correlation function, chain element-chain element pair correlation function, the mean square end-to-end distance and the mean square radius of gyration of the polymer) and (2) dynamic properties (four different autocorrelation functions, namely, the autocorrelation functions for the end-to-end distance and the radius of gyration, and the velocity autocorrelation functions for the center of mass and the end point of the chain). We found that the physical properties of the polymer chain depends sensitively on temperature. Comparison of the present work with other authors' results is also presented.

Chain Dimensions and Intrinsic Viscosities of Polypeptides in the Helix-Coil Transition Region

Jong-Ryul Kim,Tai-Kyue Ree Korean Chemical Society 1983 Bulletin of the Korean Chemical Society Vol.4 No.1

An equation is derived which correlates the unperturbed dimensions $<r^2>_0$ of polypeptides with the helical contents in the helix-coil transition region by using a simple model of a polypeptide chain. The model is a chain of connected balls which represent the repeating units, -CO-NH-CHR-, based on the fact that the repeating unit has a plane structure. The changing trend of the expansion factor ${\alpha}_{\eta}$ in the transition region is connected with the helical content $f_H$. The intrinsic viscosities [${\eta}$] of polypeptides are calculated from the unperturbed dimensions and the ${\alpha}_{\eta}$ factors. The above calculated results concerning $<r^2>_0$ and [${\eta}$] are compared with other authors' theoretical and experimental results. From the comparison, we concluded that our theory explains better the chain dimensional behavior of polypeptides in the helix-coil transition region than others.

A Method for Determining Molecular Weights of Block Copolymers by Gel Permeation Chromatography

Sohn, Jeong-In,Ree, Tai-Kyue Korean Chemical Society 1984 Bulletin of the Korean Chemical Society Vol.5 No.4

A theory is given for determining the molecular weights of block copolymers from the experimental elution volume in GPC. Interaction effect between a sample of block copolymer and a column packing material as well as the size effect are separately considered for the first time applying the partial exclusion mechanism proposed by Dawkins. The molecular weight determination shows 6${\%}$ standard-deviation from the molecular weights measured by an osmometric method for eight block copolymers, which is much more improved result than other methods, e.g., the universal plot method (13 ${\%}$) and the Runyon's method (12 ${\%}$). The reason which explains the better result is that our theory takes into account the interaction effect correctly.

Complex Formation of Syndiotactic Poly(methacrylic acid) with Complementary Polymers through Hydrogen Bonding

Kim, Bum-Sung,Jeon, Seung-Ho,Ree, Tai-Kyue Korean Chemical Society 1986 Bulletin of the Korean Chemical Society Vol.7 No.3

Complex formations between syndiotactic poly(methacrylic acid) (st-PMAA) and poly(N-vinyl pyrrolidone) (PVP), and that between st-PMAA and polyethyleneoxide (PEO) through hydrogen bonding were studied by viscometry and potentiometry. Reduced viscosity (${\eta}_{red}$) was measured at various mole fraction of PVP or PEO with respect to a constant amount of st-PMAA. Observation shows a sharp minimum at the 1:1 mole ratio of st-PMAA:PVP or st-PMAA:PEO, which shows that the complexation becomes optimal and the complex has a compact structure in this ratio. Variation of pH also supports this conclusion. This is the case of the system of st-PMAA and PVP in water as well as in DMF. Also the complexation is much enhanced when the molecular weight of PVP is high. Meanwhile, the system of st-PMAA and PEO shows a little different behavior, i.e., this system does not form the complex in DMF and does only in water. It is because the interaction st-PMAA with PEO is weaker than that with PVP.

Fourier-Transform Infrared Studies of Ionomeric Blend and Ionic Aggregation

Lee, Sang-Koog,Jeon, Seung-Ho,Ree, Tai-Kyue,Sohn, Jeong-In Korean Chemical Society 1986 Bulletin of the Korean Chemical Society Vol.7 No.4

The ionomeric blend and the ionic aggregation studies by using a Fourier-transform infrared spectroscopy(FT-IR) are presented. Two ionomers were prepared, one is barium polyacrylate and the other is barium polystyrenesulfonate. The blend of the two ionomers of the barium salts shows intermolecular ionic interaction between the carboxylated ionomer and the sulfonated ionomer. This interaction leads to considerable differences between the spectrum of the blend and the sum of the spectra of the pure ionomers. From our results, it is shown that ionic interactions must play an important role in the compatibility of the two ionomers. In the ionic aggregation study, the bands due to asymmetric stretching mode of carboxylate anion(COO-) in the carboxylated ionomer and the ionomer blend increase in intensity with increasing the divalent barium cations. These results indicate the formation of ion pairs. The doublet due to the asymmetric stretching modes of the carboxylate anion(COO-) is concerned with a sort of local structure found in the ion aggregation. By considering a possible structure for multiplets in the blend, the spectral splitting and the frequency shift are well explained.

Bond Orbital Theory of Chemical Reactivity

양강,이태규,Yang, Kang,Ree, Tai-Kyue Korean Chemical Society 1964 대한화학회지 Vol.8 No.1

종합 오비탈을 모형식으로 결합하여 분자 오비탈을 만드는 방법(linear combination of bond orbitals method, LCBO법)을 응용하여 할로겐화메탄($CH_nX_{4-n}$)과 이를 공변하는 원자(혹은 자유기)와의 추출반응(abstraction reaction $CH_nX_{4-n}\;+\;A\;{\to}\;CH_nX_{3-n}\;+\;XA$)에 대한 반응성을 연구하려는 것이 이 논문의 목적이다. 이 반응의 활성화에테르기 ${\eta}$를 계산하려고 다음과 같은 특정을 하였다. $CH_nX_{4-n}$분자가 활성화복합물로 변할때 그의 반응성 결합(reactive bond) C-X에 있는 두 전자는 완전히 이 분자의 타 ${\eta}전자계로부터 분리된다.이런 모델은 자미있는 직감적인 관념을 유인하게 되니 즉 반응성종합과 그의 주위에 있는 화학종합과의 상호작용에 의하여 ${\eta}$전자계의 반응성이 좌우된다는 것이다. 저자들의 이론적계산에 의하면 ${\eta}$는 다음식으로 표시된다. ${\varepsilon}={\zeta}+{\sum}_{i=1}^3{\eta}c-I,$ c-4 (1) Subscript C-i (i=1,2,3)는 C와 원자 i(i=H, Cl, Br, F,${\cdots}$)간의 화학결합을 표시하며 C-4 (4=(4=Cl, Br${\cdots}$) 는 반응성결합을 가르킨다. ${\zeta}$ξ는 상수한 바와 같이 완전분리상태에 있는 C-4종합과 공변원자 A간의 가상적 반응의 활성화에테르기이며 ${\eta}$C-i, C-4는 C-4와 그의 주위결합 C-i간의 상호작용에 의하여 안정화되는 에테르기를 표시한다. 결합강도와 양립하는 ${\eta}$치는 추출하여 (1)식에 대입하면 차식이 유도된다. ${\varepsilon}={\zeta}\;+\;N{\eta}c$-H, C-4 (2) N은 $CH_nX_{4-n}$분자중에 있는 C-4이상의 C-H 및 C-F결합들의 총수이다. 실험치의 ${\varepsilon}$를 N에 대하여 도시하면 $CH_nCo_{4-n}\;+\;H\;{\to}\;HCl\;+\;CH_nCl_{3-n},\;CH_nX_{4-n}\;+\;Na\;{\to}\;NaCl\;+\;CH_nCl_{3-n},\;CH_nX_{4-n} \;Na\;{\to}\;NaBr\;+\;CH_nCl_{3-n}$反應系들에 對하여 좋은 直線을 주니 (2)식이 實驗과 一致한다는 것이다 The linear combination of bond orbitals method is used to investigate the reactivity of halomethanes in abstraction reactions by atoms. The activation energy is evaluated on the assumption that, in an activated complex, two electrons in a bond to be broken become completely isolated from the rest of the ${\sigma}$-electron systems. Such a model leads to an intuitively attractive concept that the interactions between the reactive bond and the neighboring bonds govern the reactivity of ${\sigma}$-electron systems. The resulting equation for the activation energy, ${\varepsilon},\;is:\;{\narepsilon}= ${\varepsilon}={\zeta}+$$${\sum}_{i=1}^3$${\eta}c-I,$ c-4 Here, subscript C-4 indicates the bond to be broken, while C-i represents the other three bonds surrounding the reactive bond; ξ is the activation energy of a hypothetical reaction of an isolated C-4 bond and an attacking atom; and ${\eta}$C-i,C-4 stems from the stabilizing interacting of C-4 bond with neighboring C-i bonds. A choie of η′s consistent with bond strength data simplifies the above equation to a form ${\varepsilon}={\zeta}\;+\;N{\eta}c$-H, C-4 where N denotes the number of C-H plus C-F bond in halomethanes. In agreement with this equation, experimental ${\varepsilon}$-values increase linearly with increasing N.