Effect of molecular weight on the refractive index increment of polystyrenes in solution

The variation of refractive index increment $\text{d}\text{n}\text{d}\text{c}$ with molecular weight has been studied using solutions of monodisperse polystyrenes (2000<M_w<4×10⁶) in benzene. The results are in good agreement with those obtained by several authors using other systems.We have shown that the linear relationship:

$\text{d}\text{n}\text{d}\text{c}\text{=}\text{d}\text{n}\text{d}\text{c}{}_{\mathrm{m}}\text{+}\text{K″}\text{Mn}$

where $\text{(}\text{d}\text{n}\text{d}\text{c)}{}_{\mathrm{m}}$ is the refractive index increment of the repeating unit and K″ a constant, holds only for low molecular weights. With the assumption of volume additivity, we have estimated quantitatively the linear portion of the curve, $\text{d}\text{n}\text{d}\text{c}\text{=f(}\text{1}\text{M}\text{)}$, observed for molecular weights below 20 000 as a function of polymer composition. Beyond this limit, the increase of $\text{d}\text{n}\text{d}\text{c}$ with molecular weight may be probably related to segment-segment interactions within the coil.     

Pressure dependence of upper critical solution temperatures in the polystyrene - cyclohexane system

The pressure dependence of the upper critical solution temperature $\text{(}\text{d}\text{T}\text{d}\text{p}\text{)}{}_{\mathrm{c}}$ in the polystyrene-cyclohexane system has been measured over the pressure range of 1 to 50 atm. The value of $\text{(}\text{d}\text{T}\text{d}\text{p}\text{)}{}_{\mathrm{c}}$ determined over the molecular weight (M_w) range of 3.7 × 10⁴ to ～145 × 10⁴ greatly depends on the molecular weight of polystyrene. The value of $\text{(}\text{d}\text{T}\text{d}\text{p}\text{)}{}_{\mathrm{c}}$ for a polystyrene solution of low molecular weight (M_w = 3.7 × 10⁴) is positive (3.14 × 10^?3 degree atm^?1), while the values are negative (?0.52 × 10^?3～?5.64 × 10^?3 degree atm^?) for solutions of polystyrene over the high molecular weight range of 11 × 10⁴ to ～145 × 10⁴. The Patterson-Delmas theory of the corresponding state and the newer Flory theory have been used to explain this behaviour.     

Phase structure and adhesion in polymer blends: A criterion for rubber toughening

The effects of rubber particle size and rubber-matrix adhesion on notched impact toughness of nylon-rubber blends are analysed. A sharp tough-brittle transition is found to occur at a critical particle size, when the rubber volume fraction and rubber-matrix adhesion are held constant. The critical particle size increases with increasing rubber volume fraction, given by $\text{d}{}_{\mathrm{<mtext>c</mtext>}}\text{= T}{}_{\mathrm{<mtext>c</mtext>}}\text{{(}\text{π}\text{6Φ}{}_{\mathrm{<mtext>r</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}\text{? 1}}{}^{\mathrm{?1}}$, d_c is the critical particle diameter, T_c the critical interparticle distance, and ø_r the rubber volume fraction. The critical interparticle distance is a material property of the matrix, independent of rubber volume fraction and particle size. Thus, the general condition for toughening is that the interparticle distance must be smaller than the critical value. Van der Waals attraction gives sufficient adhesion for toughening. Interfacial chemical bonding is not necessary. Even if there is interfacial chemical bonding, a polymer-rubber blend will still be brittle, if the interparticle distance is greater than the critical value. The minimum adhesion required is about 1000 J m^?2, typical for van der Waals adhesion. In contrast, chemical adhesion is typically 8000 J m^?2. The present criterion for toughening is proposed to be valid for all polymer—rubber blends which dissipate the impact energy mainly by increased matrix yielding.     

Theory of adsorption of macromolecules in cylindrical pores and at surfaces of cylindrical shape

A rigorous theory of adsorption of a Gaussian chain of infinite length into cylindrically shaped pores and onto cylindrical surfaces of arbitrary diameter, D, has been developed for any energy of interaction ??. The change in the conformational free energy of a chain arriving inside the pores from an unrestricted volume is proportional to $\text{(D1)}{}^{\mathrm{?2}}$ ($\text{D1}$ is the effective pore width) over the entire molecular-sieve range (?? < ??_c). In the exclusion range (?? < 0), when the interaction of chain units with the adsorbent exhibits repulsive type forces, $\text{D1}$ is approximately equal to D. As the adsorption forces of attraction increase (0 < ?? < ??_c) the value of $\text{D1}$ increases and becomes infinite at the critical point. This makes it possible to use a single adsorbent for effective chromatographic separation of polymers over a wide range of molecular weights. In the adsorption range, where ?? > ??_c, the conformational free energy of the chain is virtually independent of the width and shape of the pores and is determined mainly by the value of ??. At the critical point, ?? = ??_c, the probability of the arrival of a polymer chain in the pore is independent of both the width and shape of the pore and is determined only by the ratio of geometrical volumes of the free volume to the pore volume. For cylindrical pores, a weak dependence of ??_c on D is observed only for narrow pores. This dependence virtually disappears on passing to adsorbents with wide pores. Consideration of the adsorption of the macromolecule on the outer surface of the cylinder showed that at any finite value of the diameter of the cylinder, D, adsorption occurs as an ‘infinite-order’ phase transition. The maximum value of the specific heat

$\text{(C}{}_{\mathrm{p}}\text{max}\text{k}\text{=}\text{25}\text{3}\text{=?}{}^2{}_{\mathrm{c}}$

does not depend on D. The degree of bonding of the macromolecule to the adsorbent increases with decreasing curvature of the surface, rapidly attaining values characteristic of chain adsorption on a plane.     

Solids mixing in a down-flow circulating fluidized bed of 0.418-m in diameter

The axial and lateral solids mixing in a down-flow circulating fluidized bed of 0.418-m diameter was investigated by a pneumatic injection phosphor tracer technique (PIPTT). The axial and lateral solids dispersion were determined by measuring the solids RTD at same axial but different lateral positions using point sources for tracer injection. A two-dimensional dispersion model described the measured RTD curves satisfactorily. The results were compared to those obtained in the small scale downers and the scale-up effect was investigated. The axial solids Peclet number Pe_a is around 110 and invariable with changing U_g, G_s and ?_s, while the lateral solids Peclet number Pe_r is linearly increasing with ?_s. And Pe_r is found to decrease with the square root of inner diameter (ID) in comparison with the results obtained in small ID downers. Correlation of Pe_r, Pe_r = (15 + 70.7 ?_s)D^− 0.5, is proposed.     

Aerated solids flow through a vertical standpipe below a pneumatically discharged bunker

An experimental investigation is described into the pneumatic discharge of sand ($\text{d}$_p = 140 μm) and of glass balk tini ($\text{d}$_p = 200 μm) from a bunker through vertical standpipes of various lengths up to 1.50 m and with diameters ranging from about 7 up to 13 mm.On the basis of a momentum balance, a relation could be established between the particle mass flow rate through the pipe, the pressure drop across the pipe, and the pipe length. In this relation two other quantities occur: the apparent density of the particulate mass, which appears to approach a limiting value with increasing pipe diameter, and the wall friction factor, which appears to be independent to pipe diameter within experimental accuracy.     

Electrochemical reduction of polymeric carbon

It was found that the electrochemical reduction of poly (tetrafluoroethylene) with lithium amalgam leading to the mixture of polymeric carbon and lithium fluoride as solid product is followed by a consecutive electrochemical reaction via a polymeric anion radical, [$\text{(}\text{?}$C_n$\text{)}\text{?}$^?]_m. The value of n was determined as 4.75 and was found to be independent of the reaction conditions. The charge of this radical is during the reaction neutralised with Li⁺ ions diffusing through the solid phase to form a chemical compound $\text{(}\text{?}$C_nLi$\text{)}\text{?}$_m whose CLi bonds have a localized character. Therefore, this compound does not evolve hydrogen in contact with water as the intercalation compounds C_nLi, but hydrolyses to a solid hydrocarbon $\text{(}\text{?}$C_nH$\text{)}\text{?}$_m.     

Dielectric loss of an oligomeric poly(propylene oxide) in the liquid region above Tg

Dynamic dielectric studies of oligomeric poly(propylene oxide) (PPO) of $\text{M}\text{?}{}_{\mathrm{n}}\text{=3034}$, between ?10° and 40°C at 0.1, 1, and 10 KHz, reveal a glass transition and a T >T_g liquid-liquid transition. Analysis of $\text{d}\text{?′}\text{d}\text{T}$ in the liquid region of PPO also indicates the presence of T₁₁. The activation enthalpies for the T_g and T₁₁ transitions have been calculated to be 39 and 18 kCal mol^?1, respectively. The T₁₁ transition in poly(propylene oxide) has been assigned to the motion of the entire polymer molecule.     

Crack growth under static and fatigue loading in glassy polymers oriented by cold-rolling

Static and fatigue crack growth in PC and fatigue crack growth in PVC have been studied using anisotropic sheets oriented by cold-rolling. Tests were carried out at room temperature for samples with various degrees of rolling reduction. In static loading for PC, a slight rolling reduction considerably improves the resistance to crack propagation in the case where the crack grows perpendicularily to the rolling direction. The measured values of crack opening displacement were compared with the Dugdale model, taking into account the effect of anisotropy. In fatigue loading for both polymers used, a power law relationship between crack growth rate $\text{d}\text{c}\text{d}\text{N}$ and stress intensity factor range ΔK, i.e., $\text{d}\text{c}\text{d}\text{N=A(ΔK)}{}^{\mathrm{m}}$ where A and m are constants, covers most of the data in spite of the differences in degrees of anisotropy. However, the constants A and m are dependent on the degree of rolling reduction. In PVC, the rolling reduction changes the fatigue fracture mode from a discontinuous growth type to continuous one. All the results show that the rolling reduction has an important effect on crack behaviour.     

Experiments on the small-strain behaviour of crosslinked natural rubber: 1. Torsion

The torsional behaviour of 1, 3 and 5 phr peroxide crosslinked natural rubber has been characterized over a range of strains from near the undistorted state (γ ≈ 0.017) to γ ≈ 1.0. Isochronal measurements of both torque and normal force were used to calculate values of the derivatives of the strain energy function W with respect to the first and second stretch invariants I₁ and I₂. In the course of our work we found that, contrary to many reports in the literature, $\text{?W}\text{?I}{}_1$ was affected significantly by the amount of crosslinking. Finally for the 1 phr peroxide crosslinked rubber it was found that, while ageing for 14 months at ambient conditions did not significantly affect the small-strain torsional modulus, $\text{G = 2(}\text{?W}\text{?I}{}_1\text{+}\text{?W}\text{?I}{}_2\text{)}$, it did significantly affect the individual derivatives $\text{?W}\text{?I}{}_1$ and $\text{?W}\text{?I}{}_2$.     

Thermal stability and structure of graphite-antimony pentachloride compounds

It is shown that antimony chloride reacting with graphite forms lamellar compounds C_12n SbCl₅ (n = 1,2,3,4,…). The identity period along the $\text{c}\text{?}$ axis is $\text{I}{}_{\mathrm{c}}\text{= 9.42}\text{A}\text{?}$ for the first stage and $\text{I}{}_{\mathrm{c}}\text{= 9.36 + (n ?1)3.36}\text{A}\text{?}$ for the other stages. Electron diffraction and X-ray studies of the hk0 reflexions with a goniometric apparatus permit to specify the structure of the compounds of n > 2. The single graphite crystals are fragmented into many ordered fields which are themselves rotated by 60°. The structure of the carbon layers remains unchanged after intercalation. The intercalated antimony pentachloride forms a hexagonal system: $\text{a = 17.23}\text{A}\text{?}\text{(2.46}\text{A}\text{?}\text{× 7)}$ the $\text{a}\text{?}$ axis being the same as the one for graphite.     

Isothermal crystallization of poly(ethylene-terephthalate) of low molecular weight by differential scanning calorimetry: 1. Crystallization kinetics

The isothermal crystallization of poly(ethylene-terephthalate) (PETP) fractions, from the melt, was investigated using differential scanning calorimetry (d.s.c.). The molecular weight range of the fractions was from 5300–11750. Crystallization temperatures were from 498–513 K. The dependence of molecular weight and undercooling on several crystallization parameters has been observed. Either maxima or minima appear at a molecular weight of about 9000, depending on the crystallization temperature. The activation energy values point to the possibility of different mechanisms of crystallization according to the chain length. A folded chain process for the higher $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ chains and an extended chain mechanism for the lower $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ chains. The values of the Avrami equation exponent n vary from 2–4 depending on the crystallization temperature; non-integer values are indicative of heterogeneous nucleation. The rate constant K depends on T_c and $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$, showing maxima related to the T_c used. The plot of log K either vs. (ΔT)^?1 and (ΔT)^?2 or $\text{T}{}_{\mathrm{<mtext>m</mtext>}}\text{T(ΔT)}$ and $\text{T}{}^2{}_{\mathrm{<mtext>m</mtext>}}\text{T(ΔT)}{}^2$ is linear in every case.     

Crystallization and melt behaviour of isotactic poly(2-vinylpyridine)

The crystallization and melting behaviour of highly isotactic poly(2-vinylpyridine) (it-P2VP) with $\text{M}\text{?}{}_{\mathrm{<mtext>v</mtext>}}\text{= 4 × 10}{}^5$ has been studied by microscopy and d.s.c.. The maximum spherulitic growth rate was found to be 250 × 10^?3μm/min at a crystallization temperature T_c of 165°C. Experimental data could be described by the growth rate theory for small supercooling, by taking the appropriate value of 75 for the constant c₂ of the WLF equation. The chain-folded surface free energy σ_e, was estimated at 39.5 × 10^?3 J m^?2. The melting curves showed 1,2 or 3 melting endotherms. At large supercooling, crystallization from the melt produced a small melting endotherm just above T_c. This peak may originate from secondary crystallization of melt trapped within the spherulites. The next melting endotherm is related to the normal primary crystallization process. Its peak temperature increased linearly with T_c, yielding an extrapolated value for the equilibrium melting temperature T°_m of 212.5°C. At the normal values of T_c and heating rate a third endotherm appeared with a peak temperature that was independent of T_c, but rose with decreasing heating rate. From the effects of heating rate and partial scanning on the ratio of peak areas, it is concluded that this peak arises from secondary crystallization by continuous melting and recrystallization during the scan. This crystallization and melting behaviour of it-P2VP is very similar to that of isotactic polystyrene.     

Raman scattering from mixtures of poly(ethylene oxide) 2000 with poly(ethylene oxide) 200

The longitudinal acoustic mode fundamental (v₁) and third harmonic (v₃) in 2000 MW PEO with both hydroxy- and methody-end-groups have been observed in the Raman spectrum as a function of 200 MW PEO oligomer content. Measurements of small-angle X-ray spacing I_x permit interpretation using a composite rod model. A good fit to the measured quantities v₁I_x and $\text{v}{}_3\text{v}{}_1$ is obtained with crystal length I_c≈9 nm, crystal modulus $\text{E}{}_{\mathrm{<mtext>c</mtext>}}\text{= 9 ×}\text{10}{}^{10}\text{N}\text{m}{}^2$ and amorphous modulus $\text{E}{}_{\mathrm{a}}\text{= 1 ×}\text{10}{}^{10}\text{N}\text{m}{}^2$. The value of Ic implies a crystalline content of ～70% for the pure polymer; the value of Ec is larger than static determinations and similar discrepancies in other materials are discussed.     

The structure of α-keratin

High-resolution low-angle meridional and near-meridional X-ray diffraction data have been collected from specimens of α-keratin and various heavy-atom derivatives of α-keratin. The observed reciprocal spacings of the layer lines satisfy the selection rule

$\text{Z=m/h+n/P+s/P}{}_{\mathrm{d}}$

where $\text{h = 67.1}\text{A}\text{?}$, $\text{P = 220}\text{A}\text{?}$, $\text{P}{}_{\mathrm{d}}\text{= 235}\text{A}\text{?}$ and m, n and s are integers. Taken in conjunction with observations on the lateral distribution of intensity this evidence suggests that the microfibrils in α-keratin have a helical structure with $\text{pitch}\text{= 220}\text{A}\text{?}$ and unit $\text{height}\text{= 67.1}\text{A}\text{?}$ which is subject to a regular axial distortion of period 235Å. Possible relationships between this helix and the coiled-coil α-helix rope segments of the constituent molecules are discussed.     

Physical characterization of suspension-crosslinked polystyrene particles and their sulphonated products: 2. Ionic networks

Strong cationic resins have been prepared from isoporous polystyrene networks in bead form with H₂SO₄ and HSO₃Cl as sulphonating agents. The effect of the reaction time of H₂SO₄ sulphonation on ion exchange capacity has been examined. The polymer-solvent interaction parameter, X, with aqueous electrolyte solutions has been calculated after minimization of electrostatic repulsions. The average molecular weight per crosslinked unit, $\text{M}\text{?}{}_{\mathrm{<mtext>c</mtext>}}$ has been measured after sulphonation and an estimation of formation of sulphone-type crosslinks has been attempted. The average size of the network structure, r_c, has been calculated as a function of the ionic strength of aqueous electrolyte solutions for networks of different molecular weight per crosslinked unit, $\text{M}\text{?}{}_{\mathrm{<mtext>c</mtext>}}$. The ion exchange capacity of the prepared resins has been measured.     

Structure and properties of poly(ethylene terephthalate) crystallized by annealing in the highly oriented state: 2. Melting behaviour and the mosaic block structure of the crystalline layers

The melting behaviour of drawn poly(ethylene terephthalate) bristles has been studied by means of differential scanning calorimetry. In addition the wide-angle X-ray diffraction pattern were analysed. For comparison some of the experiments were also carried out with undrawn samples. The differences in the melting curves of drawn and undrawn PET originate from the different crystallization kinetics. The density defect ($\text{?}{}^{\mathrm{id}}{}_{\mathrm{c}}\text{? ?1}{}_{\mathrm{c}}$) between the ideal crystal density ?^id_c and the effective density $\text{?1}{}_{\mathrm{c}}$ of the crystalline layers is a result of lattice vacancies introduced by the grain boundaries of the mosaic blocks. The relatively low ultimate crystallinity of PET is supposed to be caused by the hindrance of crystal growth of fibre direction during isothermal crystallization.     

Nucleophilic substitution onto poly(methylmethacrylate): 4. Dilute solution properties of substituted polymethacrylates

The morphological and hydrodynamic properties of a series of homogeneous fractions of substituted poly(methylmethacrylate) (A units) bearing keto-β-functional groups (B units) of the general structureCOCH₂R, with R = SO_xCH₃ (x = 1,2) or SO₂N(CH₃)₂, were investigated by intrinsic viscosity, light scattering and partial specific volume measurements in dimethylformamide (DMF) solution at 25°C. For molar substitution degrees $\text{DS}{}_{\mathrm{m}}\text{< 0.5}$, the copolymers behave as flexible random coils. The Stockmayer-Fixman-Yamakawa analysis of the $\text{[η]-}\text{M}\text{?}{}_{\mathrm{w}}$ data leads to slightly higher unperturbed dimensions K_o and steric factor σ than those for PMMA, and to stronger chain expansion as a result of the weak hydrogen bonding between DMF and COCH₂R units and a positive X_AB interaction parameter. For $\text{DS}{}_{\mathrm{m}}\text{> 0.5}$ however, copolymers bearing COCH₂SO₂N(CH₃)₂ groups behave as worm-like chains, as derived from the Fujii-Yamakawa analysis of the $\text{[η]-}\text{M}\text{?}{}_{\mathrm{w}}\text{-}\text{v}\text{?}$ data: the persistence length increases from 380 to 570 Å within the $\text{DS}$_m range 0.57–0.75. This transition from a random coil to a worm-like chain for $\text{DS}{}_{\mathrm{m}}\text{> 0.5}$ was tentatively correlated with the accumulation of B units in sterically hindered and self-associated short blocks of average length l_B ? 1.6 which provide drastically increased rigidity to the copolymer chain.     

Gasification reactivities of optical textures of metallurgical cokes

Optical textures of ten typical cokes before and after gasification in CO₂ were quantified by point counting under a polarized microscope to quantify the reactivities of each type of optical texture. Although absolute values of gasification rate for each texture varied considerably from coke to coke, their relative values were constant regardless of the origin of the cokes. The relative reactivities of flow, mosaic, isotropic and inert textures were 1,1.8,2.8 and 3.0, respectively. The relative reactivity of a single coke calculated from a knowledge of optical textures, was monotonicly correlated with the mean maximum reflectance ($\text{R}\text{?}{}_0$) of the parent coal. This indicates that the high reactivity of coke from a high-rank coal ($\text{r}\text{?}{}_0\text{= 1.8\%}$) is due to factors other than its optical texture. The crystallite height, L_c(002)' of the coke correlated with $\text{R}\text{?}{}_0$ of the parent coal, although the values of L_c(002) varied only from 1.5 to 2.1 nm.