Pulsed laser polymerization: Analytical solutions of the chain length distribution revisited

A new solution for chain‐length distributions of “dead” polymer and their moments (obtained by solving the coupled system of non‐linear differential equations in full generality) is presented and compared to existing theoretical and numerical approaches. The new solution for chain‐length distributions (cld) (at least numerically) coincides with our earlier results (analytical solution as well as data computed by use of numerical models) which were obtained by starting with strict coupling of time and degree of polymerization followed by an a posteriori Poisson broadening. (As a consequence the new solution also coincides with a numerical treatment based on fluctuating propagation probabilities by introducing an a priori Poisson broadening.) In turn, for termination exclusively by disproportionation this earlier solution is fully equivalent to Aleksandrov's approach (after some modification of the latter expression). This holds true also for termination exclusively by combination if one corrects for errors in Aleksandrov's derivation. The new solution of the moments of the cld agrees with our former results, while Aleksandrov's expressions are shown to be worthless under the usual experimental conditions.     

The Influence of Chain Length‐Dependent Propagation on the Evaluation of the Chain Length Dependence of the Rate Coefficient of Bimolecular Termination, 1. PLP–SEC Methods

Chain length distributions have been calculated for polymers prepared by pulsed laser polymerization (PLP) under the condition that not only chain termination but also chain propagation is subject to chain length dependence. The interplay between these two features is analyzed with the chain length dependence of the rate coefficient of termination k_t introduced in the form of a power law and that of propagation k_p modeled by a Langmuir‐type decrease from an initial value for zero chain length to a constant value for infinite chain lengths. The rather complex situation is governed by two important factors: the first is the extent of the decay of radical concentration [R] during one period under pseudostationary conditions, while the second is that termination events are governed by [R]² while the propagation goes directly with [R]. As a consequence there is no general recommendation possible as to which experimental value of k_p is best taken as a substitute for the correct average of k_p characterizing a specific experiment. The second point, however, is apparently responsible for the pleasant effect that the methods used so far for the determination of k_t and its chain length dependence (i.e., plotting some average of k_t versus the mean chain‐length of terminating radicals on a double‐logarithmic scale) are only subtly wrong with regard to a realistic chain length dependence. This is especially so for the quantity k_t* (the average rate coefficient of termination derived from the rate of polymerization in a PLP system) and its chain length dependence.     

Mechanical and thermal properties of rigid polyurethane foams derived from sodium lignosulfonate mixed with diethylene-, triethylene- and polyethylene glycols

Sodium salt of lignosulfonic acid (LS), which was obtained as by-product of cooking process in sulfite pulping, was solved in diethylene, triethylene or polyethylene glycol. Three series of polyurethane foams (LSPU) were synthesized by varying the LS content from 0 to 33 wt%. Apparent density (ρ) of LSPU foams ranged from 0.08 to 0.18 g cm⁻³ and was affected by both LS content and oxyethylene chain length. Glass transition temperatures increased with increasing amount of LS and with decreasing oxyethylene chain length. Thermal gravimetry analysis indicated that the LS component decomposes first and that the thermal stability increases with decreasing oxyethylene chain length. Compression strength and compression modulus increased linearly with increasing apparent density. It is concluded that LS is successfully utilized as a hard segment of rigid PU foams, whose thermal and mechanical properties can be tuned by changing the amount of LS and the length of soft oxyethylene chains.     

The Effects of Substituents and Solvents on the Ground‐State π‐Electronic Structure and Electronic Absorption Spectra of a Series of Model Merocyanine Dyes and Their Theoretical Interpretation

Two series of new merocyanine dyes have been synthesised and the dependence of their electronic structure on substituents and solvents has been studied by NMR spectroscopy, by using both the NMR ¹³C chemical shifts between adjacent C atoms in the polymethine chain and the ³J(H,H) coupling constants for trans‐vicinal protons. The widely used valence bond (VB) model based on two contributing structures cannot account theoretically for the observed alternating π‐electron density in the polymethine chain. In addition, the prediction of zero‐π‐bond order alternation (or zero‐bond length alternation) by this model is also incorrect. However, the results are consistent with the predictions of a qualitative VB model which considers the resonance of a positive charge throughout the whole polymethine chain. Based on this model and the Franck‐Condon principle the effect of substituents and solvents on the fine structure of the electronic spectra of these dyes can be explained as vibronic transitions from the vibrational state v=0 to v′, where v is the vibrational quantum number of the totally symmetric C?C valence vibration of the polymethine chain in the electronic ground state and v′ is that in the electronic excited state. In contrast, neither the effects of substituents or solvents on the electronic structure of merocyanines and their electronic spectra can be accounted for by the simple two state VB model.     

Polymerization processes at conditions of moderately short kinetic chains by calorimetry

A method has been developed for the determination of the heat of the acts of chain growth q_g and of the summary heats of the acts of chain initiation and termination q^** for the radical polymerization of vinyl monomers at the conditions of moderately short kinetic chains, when the length of the kinetic chain v < 100, but the degree of polymerization is ¯P > 20. The analysis of the experimental data, obtained by investigating the kinetics of polymerization of vinyl monomers in solution by calorimetry has led to the conclusion, that at v > 100 an approximation of the long material chains can be used (when the contribution of q^** is negligibly small) with a permissible experimental error; however, in the region of moderately short chains a correction for q^** must be introduced, in order to obtain the correct kinetics of the process.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 24, No. 6, pp. 695–701, November–December, 1988.     

The chain mechanism of ozone destruction by CFCl3 in the 214 nm photolysis of its mixtures with oxygen

The effect of CFCl₃ (0.025–0.200 mbar) addition on the formation of ozone in 214 nm photolysis of oxygen (800–2000 mbar) was investigated. Kinetic analysis of the drastic reduction in ozone formation in the presence of CFCl₃ shows that it proceeds by a chain mechanism with a chain length of 5.07 ± 0.21(2σ). This chain length is independent of CFCl₃ and O₂ pressures as well as incident light intensity and the mechanism of the chain reaction is governed by the Cl generating reactions of ClO radicals. A mechanism based only on the self reaction of these radicals: ClO + ClO → Cl₂ + O₂ (7), Cl + ClO₂ (8), and Cl + OClO (9), followed by fast decomposition of ClO₂ into Cl and O₂, predicts a chain length which is considerably lower than the observed value. Incorporation of the reaction CFCl₂O₂ + ClO → CFCl₂O + ClO₂ (11) in the mechanism satisfactorily accounts for the observed chain length. A lower limit of 3 × 10^?12 cm³ molecule^?1 s^?1 for k₁₁ is estimated.     

Formation of triblock copolymers via a tandem enhanced spin capturing—nitroxide‐mediated polymerization reaction sequence

The preparation of ABA‐type block copolymers via tandem enhanced spin capturing polymerization (ESCP) and nitroxide‐mediated polymerization (NMP) processes is explored in‐depth. Midchain alkoxyamine functional polystyrenes (M_n = 6200, 12,500 and 19,900 g mol^?1) were chain extended with styrene as well as tert‐butyl acrylate at elevated temperature NMP conditions (T = 110 °C) generating a tandem ESCP‐NMP sequence. Although the chain extensions and thus the block copolymer formation processes function well (yielding in the case of the chain extension with styrene number average molecular weights of up to 20,800 g mol^?1 (PDI = 1.22) when the 6200 g mol^?1 precursor is used and up to 67,500 g mol^?1 (PDI = 1.36) when the 19,900 g mol^?1 precursor is used and 21,600 g mol^?1 (PDI = 1.17) as well as 37,100 g mol^?1 (PDI = 1.21) for the tert‐butyl acrylate chain extensions for the 6200 and 12,500 g mol^?1 precursors, respectively), it is also evident that the efficiency of the block copolymer formation process decreases with an increasing chain length of the ESCP precursor macromolecules (i.e., for the 19,900 g mol^?1 ESCP precursor no efficient chain extension with tert‐butyl acrylate can be observed). For the polystyrene‐block‐tert‐butyl acrylate‐block‐polystyrene polymers, the molecular weights were determined via triple detection SEC using light scattering and small‐angle X‐ray scattering. © 2011 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2011.     

A study on the structural transition of a single polymer chain by parallel tempering molecular dynamics simulation

The structural transition of a single polymer chain with chain length of 100,200 and 300 beads was investigated by parallel tempering MD simulation.Our simulation results can capture the structural change from random coil to orientationally ordered structure with decreasing temperature.The clear transition was observed on the curves of radius of gyration and global orientational order parameter P as the function of temperature,which demonstrated structural formation of a single polymer chain.The linear relationships between three components of square radius of gyration R_gx²,R_gx²,R_gz² and global orientational order P can be obtained under the structurally transformational process.The slope of the linear relationship between x（or y-axis） component R_gx²(or R_gy²) and P is negative,while that of RL as the function of P is positive.The absolute value of slope is proportional to the chain length.Once the single polymer chain takes the random coil or ordered configuration,the linear relationship is invalid.The conformational change was also analyzed on microscopic scale.The polymer chain can be treated as the construction of rigid stems connecting by flexible loops.The deviation from exponentially decreased behavior of stem length distribution becomes prominent,indicating a stiffening of the chain arises leading to more and more segments ending up in the trans state with decreasing temperature.The stem length N_tr is about 21 bonds indicating the polymer chain is ordered with the specific fold length.So,the simulation results,which show the prototype of a liquid-crystalline polymer chain,are helpful to understand the crystallization process of crystalline polymers.     

n-Butane,iso-Butane and 1-Butene Adsorption on Imidazolium-Based Ionic Liquids Studied with Molecular Beam Techniques

The interaction of molecules, especially hydrocarbons, at the gas/ionic liquid (IL) surface plays a crucial role in supported IL catalysis. The dynamics of this process is investigated by measuring the trapping probabilities of n-butane, iso-butane and 1-butene on a set of frozen 1-alkyl-3-methylimidazolium-based ILs [C_nC₁Im]X, where n=4, 8 and X⁻=Cl⁻, Br⁻, [PF₆]⁻ and [Tf₂N]⁻. The decrease of the initial trapping probability with increasing surface temperature is used to determine the desorption energy of the hydrocarbons at the IL surfaces. It increases with increasing alkyl chain length n and decreasing anion size for the ILs studied. We attribute these effects to different degrees of alkyl chain surface enrichment, while interactions between the adsorbate and the anion do not play a significant role. The adsorption energy also depends on the adsorbing molecule: It decreases in the order n-butane>1-butene>iso-butane, which can be explained by different dispersion interactions.     

The effect of feed conditions in the emulsion catalytic chain transfer polymerization of alkyl methacrylates

([bis[μ-[(2,3-butanedione dioximato)(2-)-O:O′]] tetrafluorodiborato(2-)-N,N′,N″,N‴] cobalt), CoBF, has been used for the effective catalytic chain transfer of alkyl methacrylate homo- and copolymers under emulsion polymerization conditions. The catalytic chain transfer process reduces the rate of polymerization such that when the monomer is fed over 60 min the instantaneous conversion is low enough for the particle to be swollen with monomer, allowing diffusion of the catalysts between the aqueous and monomer phases. When the amount of the catalyst is reduced, the rate is increased, eventually leading to viscous, glassy particles that prevent catalyst mobility, which is observed as a breakdown in the polymerization mechanism. This can be circumvented by the addition of a 20% shot of monomer at the start of the reaction. The effective chain transfer coefficient decreases on increasing the length of the ester group of the methacrylate. The analysis of the polymers made by the technique described shows that the T_g of the polymers observe a broad transition due to the effect of chain length being pronounced at low molecular mass. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3549–3557, 1999     

Synthesis of ladder polymers containing polydiacetylene backbones connected with methylene chains and their optical properties

The polymers consisting of polydiacetylene (PDA) backbones were obtained from the novel monomer derivatives, R CC CC R′ CC CC R [where R =  (CH₂)₄OCONHCH₂COOC₄H₉, R′ =  (CH₂)_n ; n = 2, 4, 8] [4BCMU4A(n)], in which linear methylene chain is sandwiched between two diacetylene moieties by solid-state 1,4-addition reaction. The polymerization process was investigated in detail by using spectroscopic techniques such as solid-state ¹³C-NMR, visible absorption, and IR absorption spectra. It was estimated that the polymerization of 4BCMU4A(8) and 4BCMU4A(4) takes place by two consecutive 1,4-addition reactions to form two PDA backbones, which constitute the two poles of the respective ladders. The bridging methylene chain length in the monomer was found to play a vital role as far as the polymerization process is concerned. Thus, the monomers with eight or four methylene units could form the ladder–PDAs by a two-step process, whereas the monomer containing two methylene units could only undergo one-step of 1,4-addition reaction. Further, it was found that the crystallinity of the polymers depends on the methylene chain length in the monomers, 4BCMU4A(8) being the most crystalline of all. These structural features strongly affect their absorption spectra. The third-order nonlinear optical susceptibilities (χ⁽³⁾) for these polymers were measured using third-harmonic generation method. The largest χ⁽³⁾ value obtained was 3.4 × 10⁻¹¹ esu for the poly[4BCMU4A(8)] thin film in resonant region. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 3537–3548, 1999     

Modeling the Effects of Chain Length on the Termination Kinetics in Multivinyl Photopolymerizations

A model is presented that predicts photopolymerization kinetics over several orders of magnitude change in initiation rate. The model incorporates polymerization features that have long been assumed negligible when examining multivinyl photopolymerizations. The assumption that radical termination is chain‐length‐independent is relaxed by incorporating a chain‐length‐dependent termination (CLDT) parameter based on Random‐walk theory into the kinetic model. Experiments and modeling of multivinyl free‐radical photopolymerizations clearly demonstrate that CLDT is important at low conversions, where a deviation from the classical square‐root relationship between polymerization rate (R_p) and initiation rate (R_i) is observed (R_p ∝ R _i^α, α = ¹/₂, classically). At moderate conversions, when reaction diffusion dominates termination, a transition region is observed from a chain‐length‐dependent to a chain‐length‐independent region. During this transition, long chain – long chain termination is reaction diffusion controlled while the short chain – short chain termination event remains translational and segmental diffusion controlled. The scaling exponent, α, gradually increases throughout this region until achieving the classical value, where once attained, a plateau is observed. Chain‐length effects were also examined by including chain‐transfer (CT) reactions into the kinetic expressions. Upon CT agent addition, a transition region is still observed; however, at low conversion, α adheres more closely to the classical predictions. Most importantly, the model clearly demonstrates a transition from a CLDT region at low conversion to reaction diffusion controlled termination region at high conversion, where chain length is unimportant.     

The mechanism of cooxidation of isobutyraldehyde and octene-2

The mechanism of isobutyraldehyde-octene-2 cooxidation at 20°C has been investigated. The ratio of cis to trans epoxides in the reaction products shows that, at aldehyde concentrations lower than 1.0M, the epoxide is formed mainly by a radical route. The difference in the ΔH of formation of cis and trans epoxides is around 0.8 kcal/mole at 20°. The isobutyraldehyde involved in the radical epoxidation chain has been found almost quantitatively to be isopropylhydroperoxide, which is formed through the decarboxylation of i-PrCO₂· radicals, addition of oxygen, and abstraction of hydrogen atoms from the aldehyde. A rate constant of about 14 M^?1 sec^?1 at 20° has been determined for the latter reaction. The chain length for the cooxdination reaction decreases from 75 to 20 as the isobutyraldehyde concentration goes from 1.0 to 0.3M. The termination step seems to involve mainly the interaction of two i-PrO₂ · radicals. The cooxidation of octene-2 with pivalaldehyde follows a similar mechanism, but the chain length is about ten times higher under the same experimental conditions.     

The principle of corresponding states for liquid normal and branched alkanes

Prigogine's principle of corresponding states for chain-molecule liquids was tested by the determination of the characteristic volumes, temperatures, and pressures of then-alkanes from hexane through dodecane and of branched hexanes, heptanes, and octanes, using the method of Patterson and Bardin. The characteristic parameterV ^* is shown to be influenced by steric hindrance in the molecule. The quantitiesV ^* andT ^* appeared to be slightly dependent on temperature;P ^* is independent of chain length in homologous series of normal and branched alkanes.     

Molecular Weight Development in Free‐Radical Polymerization with Polyfunctional Chain‐Transfer Agents, 1. Equal Reactivity Model

The analytic expression for the weight‐average molecular weight development in free‐radical polymerization that involves a polyfunctional chain‐transfer agent is proposed. Free‐radical polymerization is kinetically controlled; therefore, the probability of chain connection with a polyfunctional chain‐transfer agent as well as the primary chain‐length distribution changes during the course of polymerization. We consider the primary chains formed at different times as different types of chains, and the heterochain branching model is used to obtain the weight‐average chain length at a given conversion level in a matrix formula, described as P_w = W { D _w + ( I + T ) SP ( I – TSP )^–1 D_f }. Because the primary chains are formed consecutively, the number of chain types N is extrapolated to infinity, but such extrapolation can be conducted with the calculated values for only three different N values. The criterion for the onset of gelation is simply described as a point at which the largest eigenvalue of the product of matrixes, TSP reaches unity, i. e., det  ( I – TSP ) = 0. The present model can readily be extended for the star‐shaped polyfunctional initiators, and the relationships between the model parameters and kinetic rate expression for such reaction systems are also shown.     

The microenvironmental effects of helical conformations of amylose: 9. Catalytic effects of amylose on the hydrolysis of p-substituted phenol esters and structural effects of substrates

Hydrolytic rate constants of p-substituted phenol esters of carboxylic acids with various chain lengths were measured in 1:1 (v/v) Me₂SO-H₂O. Amylose accelerates the hydrolytic rates of all substrates, but the catalytic patterns are different for long and short chain substrates, i.e., acetates (2-X) show 2nd order kinetics, dodecanoates, (12-X) and hexadecanoates (16-X) follow Michaelis-Menten saturation kinetics. The dissociation constants K_d of inclusion complexes are dependent on the chain length of substrates. The rate constants k_un, K_obs, k₂ and k_o of 12-X and 2-X conform to the Hammett relation, the ρ values are almost the same, whether in the presence or absence of amylose. But k_un, k_obs and k_c values of 16-X all cannot be correlated by the Hammett equation because of the aggregation and self-coiling of 16-X in this poor solvent. Thermodynamic parameters ΔH_i and ΔS_i of the inclusion process and activation parameters ΔH_c^≠ and ΔS_c^≠ were obtained from the temperature dependence of K_d and k_c. The results indicate that the formation of inclusion complexes between amylose and substrates is an entropy disfavored and enthalpy favored process. Comparison of ΔH_c^≠, ΔS_c^≠ with ΔH_un^≠ and ΔS_un^≠ shows that the acceleration of hydrolysis of long chain substrates by amylose is caused by the formation of helical inclusion complexes.     

Distributions of the unperturbed dimensions of Markov-chain copolymers

This investigation shows that Markov-chain copolymers can be regarded as random copolymers the segment lengths of which depend on the copolymerization parameters. It was possible to derive simple analytical formulae for the mean-square end-to-end distance (〈r²〉), the Kuhn length, and the distribution of r² under theta-conditions. The results of these equations are in excellent agreement with data from simulations. It is shown that 〈r²〉 as well as the non-uniformity of r² increase strongly with increasing probabilities of homopropagation, i.e., with increasing mean homosequence lengths. Furthermore it is demonstrated by simulation that even chains of identical length and composition show a distribution of r² because of different arrangements of the sequences inside the chains. For chains or chain segments shorter than the average homosequences, a double-peak distribution of r² is found. The equations derived in this paper can be applied to real copolymers as well as to chains the curvature of which is altered locally by the association of ligands.     

Elastic behavior of bimodal poly(dimethylsiloxane) networks

The rubberlike elastic behavior of bimodal poly(dimethylsiloxane) (PDMS) networks was investigated by the Monte Carlo simulation method and enumeration calculation method on the basis of the rotational‐isomeric‐state (RIS) model. These bimodal PDMS networks consist of short chains (chain length from 10 to 20) as well as long chains (chain length equal to 150). For long PDMS chains, through generating many PDMS conformations in the equilibrium state using the Monte Carlo simulation method we can obtain the average Helmholtz free energy and the average energy. For short PDMS chains with chain lengths from 10 to 20, as the total number of conformations is only from 6.56 × 10³ to 3.87 × 10⁸, we adopt the enumeration calculation method. The deformation is partitioned nonaffinely between the long and short chains, and this partitioning can be determined by requiring the free energy of the deformed network to be minimized. Chain dimensions and thermodynamic statistical properties of bimodal PDMS networks at various elongation ratios are discussed. We find that elastic force f increases with elongation ratio λ; the energy contribution f_u to elastic force is significant, and the ratio of ranges from 0.15 to 0.36 at T = 343 K. In the meantime, elastic force f increases with the average energy 〈U〉. The energy change in the process of tensile elongation is taken over, which has been ignored in previous theories. Our calculations may provide some insights into the phenomena of rubberlike elasticity of bimodal networks. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 105–114, 2002