Mechanics of peeling of rubbery materials. I. Peel strength and energy dissipation

The peel strength found in the trousers-type peeling process is treated for the case in which the adherends, assumed to be flexible but inextensible are bonded by rubbery viscoelastic adhesives. Taking into consideration energy dissipation during deformation of the adhesive, Griffith's criterion is extended to the peeling of viscoelastic materials. For the peeling force per unit width f it is deduced that 2f = Γ + u′h, where T is twice the surface energy, u' is the energy dissipation per unit volume of adhesive, and h is the thickness of the adhesive layer. Values of u' obtained from peeling tests for various thicknesses are compared with those from the tensile tests and found to agree with the above relation. The deduction that the peel strength is independent of the thickness for adhesives with no energy dissipation is also verified experimentally.     

Force variation of chlorinated butyl-rubber peeling from steel in the process of vulcanization

Vulcanization of an adhered layer with the use of low-temperature vulcanizing agents with different adhesion activities was carried out to increase the heat resistance and resistance to displacement of the adhesive tapes with different adhesive activity. It is shown that the force variation of the vulcanized adherent layer based on the chlorobutyl rubber and polymeric petroleum resin for peeling from steel depends on the measurement temperature: at 25°C, the peeling force decreases, while at 80°C it increases as compared with nonvulcanized adhesive. The observed changes are conditioned both by the increase of the cohesion strength of the adhered layer and by decrease of the elastic component in the layer peeling energy.     

Liquid crystalline main chain polymers with a poly(p-phenyleneterephthalate) backbone. 2. Fiber spinning and mechanical properties of polyesters with alkoxy side chains

Fiber spinning and mechanical properties of four rigid polyesters with alkoxy substituents of different length and placement were evaluated. Properties of oriented fibers from the polymer with dodecyloxy substituents on the terephthalate moiety, PTA12HQ, were significantly affected by the crystal modification. At room temperature the following properties (tensile modulus E, tensile strength σ_b, and strain at break ε_b) could be obtained: E = 9.5 GPa, σ_b = 85 MPa and ε_b = 1.1% for phase L_f (the “frozen in layered mesophase”); E = 10.4 GPa, σ_b = 59 MPa and ε_b = 0.6% for modification A; E = 17.3 GPa, σ_b = 158 MPa and ε_b = 1.2% for modification B. Because of the higher amount of main chains per cross sectional area the polymer with hexyloxy side chains, PTA6HQ, showed better properties at a comparable degree of molecular orientation: E = 24 GPa, σ_b = 270 MPa, ε_b = 1.4%. Fibers obtained from the polyester with dodecyloxy substituents on the hydroquinone moiety, PTAHQ12, were too brittle to handle. The polyester with dodecyloxy substituents on both moieties, PTA12HQ12, was spun from the isotropic melt. Because of the obtained low degree of orientation, properties (E = 1 GPa, σ_b = 40 MPa, and ε_b = 6.3%) were governed by interactions between the chains (the main chains are not load-bearing). © 1993 John Wiley & Sons, Inc.     

Adhesion of viscoelastic materials to rigid substrates. III. Energy criterion for failure

Measurements are described of the strength of a model adhesive joint subjected to (1) tensile rupture, with the interface containing a small unbonded region of varying size, and (2) pure shear deformation, in the form of a partly unbonded sheet. These, and previous measurements of resistance to peeling separation, are all shown to be consistent with an energy criterion for adhesive failure. The characteristic failure energy per unit area of interface has been determined for the model adhesive material as a function of the effective rate of detachment, over a wide range covering almost the entire spectrum of viscoelastic response. The values obtained are found to increase from levels only slightly higher than thermodynamic considerations would predict, i.e., 10²?10³ ergs/cm², at low rates of crack propagation, up to a value of about 10⁶ ergs/cm² at high rates when the material responds in a glasslike manner. These results suggest that the failure energy has two components: the (reversible) work of adsorption and the (irreversible) work of deformation of the adhesive in effecting separation.     

THE PHOTOEXCITED TRIPLET STATE OF TETRAPHENYL CHLORIN, MAGNESIUM TETRAPHENYL PORPHYRIN AND WHOLE CELLS OF CHLAMYDOMONAS REINHARDI. A LIGHT MODULATION-EPR STUDY

Abstract— The photoexcited triplet states of frozen solutions of tetraphenyl chlorin (TPC), magnesium tetraphenyl porphyrin (MgTPP) and whole cells of Chlamydomonas reinhardi have been studied by light modulation-EPR spectroscopy. The porphyrins were chosen to be studied as model compounds for chlorophyll molecules, From EPR spectra the zero field splitting parameters (ZFS) were calculated. For TPC, |D| = 0.0364 ± 0.0002 cm^-1, |E| = 0.0063 ± 0.0002 cm^-1. For MgTPP, |D| = 0.0310 ± 0.0002 cm^-1. For chloroplasts, |D| = 0.0280 ± 0.0004 cm^-1, |E| = 0.0032 ± 0.0004 cm^-1. In all compounds studied, except MgTPP, electron spin polarization (ESP) was observed. From the analysis of the kinetic curves at each canonical orientation we evaluated the spin lattice relaxation rate W, the depopulation rate constants k_p, and the ratio between the population rate constants, A_p, at zero magnetic field. For TPC in ethanol-toluene (5:1) k_x= (0.70 ± 0.10) × 10³ s^-1, k_y= (0.40 ± 0.07) × 10³ s^-1, k_x= (0.24 ± 0.05) × 10³ s^-1; A_x:A_y:A_z? 1.0:0.6:0.4; W= (2.60 ± 0.40) × 10³ s^-1. For MgTPP, only the total decay rate constant, k_T, was calculated: (1.5 ± 0.2) × 10 s^-1 in n-octane and (4.8 ± 0.8) × 10 s^-1 in ethanol. The results for TPC and MgTPP are compared to those reported previously for chlorophyll. It is concluded that the dynamics of the photoexcited triplet state in chlorophylls are mainly governed by the chlorin macrocycle. From the EPR spectrum and ZFS parameters of chloroplasts, we propose that both chlorophyll a and chlorophyll b are the main constituents of the EPR spectrum. From the analysis of the kinetic curves we obtain separately the kinetic parameters for chlorophylls a and b, k^a_x= (1.30 ± 0.20) × 10³ s^-1, k^a_y;= (0.85 ± 0.15) × 10³ s^-1k^a_x= (0.32 ± 0.05) × 10³ s^-1; A^a_x:A^a_y:A^a_z? 1.0:0.7:0.2; W^a= (1.20 ± 0.20) × 10³ s^-1; k^b_x= (0.56 ± 0.09) × 10³ s^-1, k^b_y= (0.30 ± 0.04) × 10³ s^-1, k^b_z= (0.06 ± 0.01) × 10³ s^-1; A^b_x:A^b_y:A^b_x? 1.0:0.6:0.1; W^b= (5.00 ± 0.80) × 10³ s^-1. These results are very close to those found separately for chlorophyll a and chlorophyll b oligomers in vitro.     

Gel formation with multiple interunit junctions. I—Molecules carrying different functional groups

Number‐ and weight‐average molecular weight of condensation polymers formed by primary molecules carrying different species of functional groups {A_i} (i = 1, 2, …, s) are derived by cascade theory. These functional groups are allowed to form multiple junctions of variable multiplicity k. The gel point condition is found to be given by ∑ w_i/|μ_w,i + 1/∑ f_i ? 1 = 0, where f_i is the number of A_i groups specified by the index i on a primary molecule, w_i ≡ f_i/∑ f_i the number fraction of the species i it carries, and |μ_w,i the weight average multiplicity of the junctions formed by the groups A_i. The explicit form of the molecular weight distribution function is found for the simplest case of two components. Possible application to thermoreversible gelation is suggested. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2405–2412, 2003     

Investigation of shear failure mechanisms of pressure‐sensitive adhesives

We report new experiments investigating the failure mechanisms in shear, of thin layers of acrylic pressure‐sensitive adhesives (PSA). We have developed a novel experimental device able to shear a soft adhesive layer confined between a rigid hemispherical lens and a rigid glass substrate. Using the resources of in situ contact visualization, the nonhomogeneous deformation of the layer and the shear failure processes were observed optically. Depending on the rheological properties of the adhesive, ratios of the contact radius over the layer thickness of 10–30 were achieved, mimicking well the contact conditions encountered in a thin adhesive layer within a joint. When the adhesive was weakly crosslinked, we observed a fluid‐like behavior and could measure a reasonable value for the viscosity of the PSA, implying that flow can occur in the layer and failure will occur by creep. On the other hand, for a more crosslinked adhesive, closer to what is used in applications, a stick‐slip peeling behavior was observed, which involves a coupling between peeling mechanisms at the leading edge of the contact and interfacial slippage. Such a process suggests a failure by fracture rather than by creep. Interestingly, the peeling mechanisms and the associated stress levels change significantly when the layer becomes as thin as 20 μm, implying a fracture process that is controlled by a critical energy release rate in shear G_IIc rather than by a critical shear stress causing failure of the interfacial bonds. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3316–3330, 2005     

Surface grafting of polyethylene by mutual irradiation in methyl acrylate vapor. III. Quantitative surface analysis by x-ray photoelectron spectroscopy

X-ray photoelectron spectroscopy (ESCA) has been used for quantitative surface analysis of surface grafts prepared by mutual irradiation of polyethylene (PE) in methyl acrylate (MA) vapor with γ rays and high-energy electrons. The binding-energy shift between the C_1s electrons in the ester group of poly(methyl acrylate) (PMA) and in PE is large enough (ca. 3.6 eV) to distinguish the PMA and PE components. The C_1s peak-area ratio of ester carbon to other carbons is related quantitatively to graft composition by constructing a calibration curve for a given instrument and excitation source, with a series of homogeneous grafts of known composition used as the calibration standards. Using the calibration curve and the measured peak ratio, the surface composition of the surface grafts is determined. The relations between surface compositions according to ESCA and attenuated total reflection (ATR) infrared spectroscopy and between adhesive bond strength and ESCA composition are discussed. In the electron-induced grafts, the grafted surface reaches maximum adhesive bondability with attainment of 100 mole % MA in the surface detected by ESCA; i.e., with formation of a homopolymer layer. The ESCA composition can be used as an indicator of the presence of the homopolymer layer or as a criterion for predicting adhesive bond strength.     

Roughness and anisotropy effects on wettability of polytetrafluoroethylene and sodium-treated polytetrafluoroethylene

The effect of roughness on wettability of skived polytetrafluoroethylene (PTFE or Teflon) and Na-treated PTFE film were studied by advancing contact angle measurements. The effect of an anisotropic force field of elongated Na-treated PTFE on the shear bond strength were also studied as a function of elongation. The results are analyzed in terms of London dispersion γs^d and Keesom polar γs^p contributions to surface energy γs. It was found that the roughness effect on wettability of PTFE is significant for untreated PTFE and negligible for Na-treated PTFE. Our shear bond strength σ_b analysis of elongated Na-treated PTFE showed that σ_b is influenced by an anisotropic force field and the σ_b increases with the fractional polarity p = γs^p/γs but decreases with the dispersion fraction d = γs^d/γs of solid-vapor surface tension γs = γs^d + γs^p     

Effects of spinning conditions on the mechanical properties of ultrahigh‐molecular‐weight polyethylene fibers

We investigated the tensile strength and modulus of ultrahigh‐strength polyethylene (UHSPE) fibers obtained by using the special two‐step‐drawing process of as‐spun fiber (ASFs) which were prepared by the so‐called gel‐spinning method. We have found that the higher the ASF's spinning speed is, the higher the attainable tensile strength σ_f and modulus E are. For all the fibers drawn from ASFs with various spinning speed except for 120 m/min, we have found a master curve for the inverse of σ_f which is plotted as a function of T^1/4E^?1/2, where T is the linear density of the drawn fibers, in consistent with the Griffith theory: a thicker fiber obtained with a lower spinning speed exhibits lower strength, although all the AFSs possess the same value of E. This also suggests that a thicker fiber contains more defects which would lead to the Griffith‐type crack propagation breakage. Moreover, from morphological observation of ASFs under transmission electron microscopy, the ASF obtained at a relatively low spinning speed possesses a heterogeneous cross‐sectional morphology, whereas that obtained at relatively high spinning speed possesses a relatively homogenous morphology. We propose that this morphological evidence may account for the experimental findings of the behavior of the mechanical properties described above. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2639–2652, 2005     

Ultimate tensile properties of elastomers. VII. Effect of crosslink density on time–temperature dependence

Data on tensile strength and elongation at break for a series of Viton A-HV vulcanizates are discussed. The data were obtained at various extension rates at temperatures from ?5 to 230°C (25 ? T — T_g ? 260°C) on seven vulcanizates having crosslink densities v_e (estimated from C₁ in the Mooney-Rivlin equation) from 0.46 × 10^?5 to 24.4 × 10^?5 mole/cm³. At an extension rate of 1 min^?1, an increase in v_e affects the tensile strength σ_b (based on the undeformed cross-sectional area) and the true tensile strength σ_bσ_b (based on the cross-sectional area of a deformed specimen) as follows: σ_b is essentially constant at a low temperature; it passes through a decided maximum at intermediate temperatures; and it increases to a plateau at elevated temperatures. In contrast, λ_bσ_b decreases markedly at all temperatures, an exception being the most lightly crosslinked vulcanizate(s). Application of time—temperature superposition to the ultimate-property data gave log a_T; its temperature dependence is that typical of nonpolar rubbery polymers. Data on the vulcanizates were compared in corresponding temperature states by plotting log 273σ_b/T, log 273λ_bσ_b/T, and (λ_b — 1)/(λ_b — 1)_max against logt_b/(t_b)_max, where t_b is the temperature-reduced time to break and (t_b)_max is the value at which the ultimate extension ratio λ_b attains its maximum, (λ_b)_max. Except for the most lightly crosslink vulcanizate, the comparison shows that 273λ_bσ_b/T and (λ_b — 1)/(λ_b — 1)_max are substantially independent of (or only weakly dependent on) crosslink density, that 273λ_b/T increases with v_e, and that 273λ_b/T ∝? v_e^0.6 and λ_b ∝? v_e^?0.4 at a large value of t_b/(t_b)_max.     

Zone‐Drawn Poly(p‐phenylene) Films. Effects of Molecular Orientation on Electrical and Mechanical Properties

The electrochemically synthesized poly(p‐phenylene) film could be zone drawn by a factor of 1.57, where the orientation function (f) increased with the draw ratio (λ), regardless of the heater temperature (T_h) or applied tension (σ), and reached 0.428 for the resulting film. The electrical conductivity in the drawing direction rose with f but decreased as T_h became higher due to dedoping that occurred simultaneously with drawing. Young's modulus and tensile strength significantly increased to 4.5 GPa and 155 MPa by zone drawing from 1.1 GPa and 79 MPa of the as‐synthesized film.     

Effect of length and number of interlinking molecules on the strength of adhesion

The fracture energy G of an adhesive bond appears to be a product of two terms: G = G_O [1 + f(R, T)], where G_O is the intrinsic (chemical) strength of the interface and f(R, T), usually much larger than unity, reflects energy dissipated within the adherends at a crack speed R and temperature T. Values of G_O have been determined for interlinked sheets of an SBR elastomer by measuring the peel strength at low rates and high temperatures, and in the swollen state, to minimize internal losses. Both the density ΔN and molecular length L of interlinking molecules were varied. G_O was found to increase in proportion to (ΔN)L^3/2, in accord with the molecular theory of Lake and Thomas. As the peel rate was raised and the test temperature lowered, G was considerably increased by internal dissipative processes, becoming as much as 1000 × G_O near the glass transition. The loss function f(R, T) was found to depend somewhat upon the strand length L, being about twice as large at intermediate peel rates when L was increased by 40%. It also depended on the density ΔN of interlinking molecules, being about twice as large at high peel rates when the density of interlinks was reduced by a factor of six. Thus, the loss function f(R, T) is greater when the interlinking molecules are few and long, and it is lower when they are many and short. However, it is mainly governed by two parameters: peel rate R and temperature difference (T − T_g), in accord with a viscoelastic loss mechanism. © 1996 John Wiley & Sons, Inc.     

Reusable antifouling viscoelastic adhesive with an elastic skin

Although the viscoelasticity or tackiness of a pressure-sensitive adhesive gives it strength owing to energy dissipation during peeling, it also renders it nonreusable because of structural changes such as the formation of fibrils, cohesive failure, and fouling. However, an elastic layer has good structural integrity and cohesive strength but low adhesive energy. We demonstrate an effective composite adhesive in which a soft viscoelastic bulk layer is imbedded in a largely elastic thin skin layer. The composite layer is able to meet the conflicting demands of the high peel strength comparable to the viscoelastic core and the structural integrity, reusability, and antifouling properties of the elastic skin. Our model adhesive is made of poly(dimethylsiloxane), where its core and skin are created by varying the cross-linking percentage from 2 to 10%.     

Studies in mass spectrometry. I—Common intermediates in the fragmentation of isomeric compounds under electron-impact

In the particular case where a specific ion [c]^+· is generated with different internal energy, the variation of Z(E) = [(f)⁺]/[(c)^+·] vs energy of the electron beam is discussed in relation to the P(E_i) and k(E_i) functions which describe the decay process [c]^+· → [f]⁺. Qualitative application to seven isomeric hydrocarbons suggests that, among these isomers, two pairs might rearrange to a common intermediate before fragmentation occurs. It is found that in such cases the curves Z = f(E) for a given fragmentation are not superimposable but parallel, as suggested by theoretical considerations.     

Peel adhesion and viscoelasticity of rubber–resin blends

Mixtures in various proportions of natural rubber (NR) and each of two tackifier resins, a poly-β-pinene and a modified pentaerythritol rosin ester, were used as the adhesive layer in joining a flexible polyester strip to a plane glass substrate. Measurements of the force required to peel the strip from the glass at a 90° angle were made over a range of pulling rates at several temperatures. Application of time-temperature superposition enabled a master curve of (reduced) peel force versus (log) pulling rate at a standard temperature (296 K) to be obtained for each adhesive composition. The master curves showed, in increasing order of pulling rate, some or all of four different modes of peeling: (i) peeling with viscous adhesive response, (ii) peeling with rubbery response, (iii) oscillatory or slip-stick peeling, and (iv) peeling with glassy adhesive response. In general, transitions between the different peeling modes were quite abrupt. Increase in concentration of tackifier resin caused displacement of the master curve toward lower pulling rates [an effect interpreted in terms of an increasing adhesive glass temperature (T_g)], and a superimposed displacement of the transition between peeling modes (i) and (ii) toward higher pulling rates-an effect attributed to reduction in adhesive average molecular weight. The influence of the tackifier resin in modifying the viscoelastic characteristics of the adhesive was further demonstrated in a comparison of the peel force master curves with corresponding master curves of dynamic storage modulus.     

分子亲脂-亲水性的量子化学描述II. 氨基酸侧链的亲水指标和亲脂指标

在启发式亲脂势HMLP (heuristic molecular lipophilicity potential)的基础上提出了分子、分子片段和原子的亲水指标和亲脂指标. 计算出了20个天然氨基酸侧链的亲水、亲脂指标和亲水、亲脂表面积, 并用线性自由能函数表达氨基酸侧链的溶剂化自由能, ΔG_sol,i^θ＝b₀＋b₁L_i＋b₂H_i＋b₃S_i^＋＋b₄S_i^－. . 应用线性自由能函数和氨基酸侧链的亲水和亲脂指标, 计算了20个氨基酸残基的3种相转移自由能(蒸气-水、蒸气-正辛醇、正辛醇-水)和正辛醇-水分配系数logP_ow, 取得了与实验值高度一致的良好效果. HMLP的亲水和亲脂指标是HMLP的指标化, 扩展了这一方法的使用范围. 氨基酸侧链的亲水、亲脂指标和线性自由能函数有望用于生物大分子受体与配体的结合自由能的估算、蛋白质的结构与功能、蛋白-蛋白相互作用和识别的研究.     

Mass transfer from copper melts by top-blowing of an argon-hydrogen plasma jet

The volatilization of lead, copper, tin, and zinc from copper melts using the technique of top-blowing with an argon-hydrogen plasma jet was experimentally investigated and theoretically evaluated. A plasma burner with 16 kW power was used in the experiments. The mole flow of the plasma gases was 0.017 mol/s (25 liters/min when T = 25°C and P_G = 1 bar). The temperature was 1830°C on the surface of the melt and between 1200 and 1500°C in the molten solution. When the zinc concentration is above 2 mole%, supersaturation of zinc occurs on the surface. In this range of concentrations the ratio of dilution of the concentration in relation to time is linear (zeroth-order reaction). When the concentration of zinc is below 2 mole%, the time dependence of volatilization can be described by an exponential law corresponding to a first-order reaction, because in this case the rate-determining step is the mass transport of zinc in the molten copper phase. From the change from zeroth-order to first-order reaction during the volatilization of zinc, the temperature on the surface of the melt can be estimated with a high degree of accuracy. On the other hand, the volatilization of tin and lead is determined by mass transfer in the gas phase, which leads to an exponential law for the whole range of concentrations. Reaction models were set up on the basis of the experimental data. The relationships thereby obtained permit one to evaluate in advance the yield of future industrial volatilization processes with top-blown plasma jets.Nomenclature A activity - A _e , m² effective mass-transport or mass-transfer area - k, mol/m² s^–1 mass-transfer coefficient - k _g , mol/m² s^–1 mass-transfer coefficient in the gas phase - k _s , mol/m² s^–1 mass-transfer coefficient in the melt phase - k, mol/m² s^–1 overall mass-transfer coefficient - K =P _i /x _i equilibrium coefficient (distribution coefficient) - K _T =P _i /a _i equilibrium coefficient - n _s , mol number of moles of the melt phase - n _G , mol number of moles of the gas phase - n _g , mol/s mole flow of the top-blown gas - n _i , mol/s mole flow of the extract i into the gas phase - P _i , N/ M² partial pressure of extract substance i in the gas phase - t, s time - T, °C or K temperature: T_s, in the melt; T , at the phase interface - x _i , mol/mol concentration in the melt - X _f ¹ , mol/mol concentration in the melt at the phase interface - w, s^–1 rate constant - y _i , mol/mol concentration in the gas phase - y _f ⁱ , mol/mol concentration in the gas phase at interface - z, m coordinate in the direction of mass transfer - activity coefficient - ^O Henry coefficient     

DAMAGE OF SILICONE RUBBER INDUCED BY PROTON IRRADIATION

In this paper, the damage to methyl silicone rubber induced by irradiation with protons of 150 keV energy wasstudied. The surface morphology, tensile strength, Shore hardness, cross-linking density and glass transition temperaturewere examined. Positron annihilation lifetime spectrum analysis (PALS) was perfomed to reveal the damage mechanisms ofthe rubber. The results showed that tensile strength and Shore hardness of the rubber increased first and then decreased withincreasing irradiation fluence. The PALS characteristics τ_3 and I_3, as well as the free volume V_f, decreased with increasingirradiation fluence up to 10~(15) cm~(-2), and then increased slowly. It indicates that proton irradiation causes a decrease of freevolume in the methyl silicone rubber when the fluence is less than 10~(15)cm~(-2), while the free volume increases when thefluence is greater than 10~(15)cm~(-2). The results on cross-linking density indicate that the cross-linking induced by protonirradiation is dominant at smaller proton fluences, increasing the tensile strength and Shore hardness of the rubber, while thedegradation of rubber dominates at greater fluence, leading to a decrease of tensile strength and Shore hardness.     

Folded chain crystals as micro-phases

Summary A thermodynamic treatment of homo-polymer systems out of linear chains with folded chain crystals is developed outgoing from appropriate models for single component systems. An expansion of thermodynamics to multi-micro-phase systems the structure of which is partially or totaly frozen is indispensable. General properties of melt crystallized homopolymers with folded chain crystals can be recognized indeed when the thermodynamic formalisms developed are applied.

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Zusammenfassung Das Schmelzen in polymeren Einteilchensystemen mit Faltungskristallen einheitlicher Dicke kann thermodynamisch als Umwandlung 1. Ordnung in einer Richtung behandelt werden, wenn die Faltungslänge bis zur Umwandlungstemperatur konstant bleibt (Faltungslänge als innerer Zusatzparameter). Eine wesentliche begriffliche Erweiterung ist für eine phänomenologische Beschreibung mit den Mitteln der Thermodynamik unumgänglich, wenn eine Faltungskristallit-Dickenverteilung existiert, weil dann prinzipiell nur noch partielle Koexistenz bestimmter Fraktionen metastabiler autonomer Mikrophasen mit der Schmelze möglich ist. Partielles Aufschmelzen und Rektistallisation können so dann auch in Betracht genommen werden. Die entwickelten Konzeptionen bewähren sich in der Anwendung auf bekannte Experimente.

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Notation g ^c (y);g ^m (Y) molar Gibbs-free energy of a chain of a lengthy within an extended chain crystal and the melt rsp - g _o ^c ;g _o ^m molar free enthalpy of the unit in the crystal lattice and the melt rsp - g(y,y, f) molar Gibbs-function of an ideally folded chain crystal with the fold heighty _f - gco(y, y _ef,y _f) molar free enthalpy of the crystal corey _co - g ₀ ^ex ((y_ef) excess free enthalpy of the longitudinal layers of folded chain crystals - g ^f(y_ef,g _o ^ex ) molar free enthalpy of the longitudinal layers of the folded chain crystals - g ^tot molar free enthalpy of a chain of the lengthy within a folded chain crystal with longitudinal layers - h _o ^1c ,h _o ^m molar enthalpy of the chain unit within the crystal lattice and the melt rsp - h =h _o ^m -h _o ^c molar heat of fusion of the unit - C _p=C _p ^m -C _p ^c difference of the molar specific heat of a unit within the melt and within the chain crystal - h ^D molar defect enthalpy of local defects within the crystal lattice - h ^D molar defect enthalpy of the unit - s _o ^c ,s _o ^m molar entropy of the chain unit within the crystal lattice and the melt rsp - s _c ^m conformational entropy of a chain in the melt - s _gk conformational entropy of a chain of lengthy within a super-lattice as indicated in figure 5, - s molar entropy of fusion of the melt - s _n ^c nematic configurational entropy - T absolute temperature - T _M melting temperature of extended chain crystals of infinite size - T _M(y) melting temperature of extended chain crystals containing only chains of the lengthy - T _M (y, y _f) melting temperatureof folded chain crystals of the thicknessy _f composed of chains of the lengthy - T _M(y _f) melting temperature of folded chain crystals of the thicknessy _fy - _eh excess free enthalpy of the chain ends occupying crystallographic places - _ef excess free enthalpy of a single fold loop - z coordination number of the lattice - 7 Euler's constant - R Boltzmann's constant - y number of chain units - y _f height of lamelliform folded chain crystals - f=(y/y _f - 1) number of fold loops of a chain of a lengthy when being built into a folded chain crystal of the thicknessy _f - y _co thickness of the crystal core of the simplified twophase model - y _et average thickness of the surface layers of folded chain crystals - N _c number of crystallized units of a chain of the lengthy - x _c molar number of crystallized units of a chain of the lengthy - x _nc molar number of noncrystallized units - excess free enthalpy parameter - (y _f) thickness distribution of the fold heightsy _f With 15 figures and 2 tables