Studies of cyclic and linear poly(dimethyl siloxanes): 1. Limiting viscosity number-molecular weight relationships

The limiting viscosity numbers of ten cyclic and ten linear poly(dimethyl siloxane) fractions have been measured in a π-solvent (butanone at 293K) and in two ‘good’ solvents (toluene and cyclohexane at 298K). The dimethyl siloxane fractions studied were in the molecular weight range $\text{800 <}\text{M}\text{?}{}_{\mathrm{w}}\text{< 17 000}$. The data obtained are compared with related studies published in the literature. The ratio of the limiting viscosity numbers [η]_r and [η]_l of the cyclic and linear poly(dimethyl siloxanes) with $\text{M}\text{?}{}_{\mathrm{w}}\text{> 2500}$ was found to be 0.67 in butanone at 293K. This value is identical (within experimental error) to the theoretical ratio $\text{[η]}{}_{\mathrm{r}}\text{[η]}{}_{\mathrm{l}}\text{= 0.66}$ predicted by Bloomfield and Zimm and others for ring and chain polymers in π-solvents. The ratio $\text{[η]}{}_{\mathrm{r}}\text{[η]}{}_{\mathrm{l}}$ was found to be somewhat smaller for the higher molecular weight polymers in the ‘good’ solvents.     

Sedimentation velocity measurements close to the upper critical solution temperature and at θ-conditions: polystyrene in cyclopentane over a large concentration interval

Sedimentation velocity measurements on polystyrene (M = 110 000) in cyclopentane over an extended concentration region and from 5°C (close to the upper critical solution temperature) to 40°C are reported. The concentration dependence parameter (k_s)_w increases from 2 to 5°C to 27 at 40°C. For all temperatures except 5°C, $\text{s}{}_0\text{s}$ vs. w[η]_w shows an upward curvature at w[η]_w ≈ 1; at 5°C, on the other hand, $\text{s}{}_0\text{s}$ is independent of concentration over the region considered. Furthermore, measurements have also been performed at 20°C (θ-conditions) over a large concentration interval for the molecular weights M = 20 400, 390 000 and 950 000. The parameters s₀ and (k_s)_w were both found to be proportional to $\text{M}\text{?}{}^{\mathrm{1/2}}{}_{\mathrm{w}}$. In the ‘hydrodynamically normalized’ plot $\text{s}{}_0\text{s}$ vs. w[η]_w the sedimentation behaviour can approximately be represented by a single curve for all the molecular weights.     

Solid and liquid state relaxations in spin-labelled poly)ethylene glycol) at high temperatures (T>Tg)

Free and covalently bonded (esterified) nitroxyl radicals experienced in poly(ethylene glycols) (PEG; $\text{M}\text{?}{}_{\mathrm{n}}$ 200–22 000) at temperatures T >T_g several different isotropic rotational relaxation regions. As a first approximation it was assumed, that in the polyglycols $\text{M}\text{?}{}_{\mathrm{n}}\text{? 1000}$ there are at least three rotational relaxation regions: the liquid state (I), the melting state (II) and the solid state (III). The existence of the fourth region, the frozen solid state (IV), was also concluded. The existence of the relaxation region (II) indicated the close interaction between radicals and the crystalline phase. The order of rotational activation energies (E_a) was E^II_a >E^III_a >E^I_a >E^IV_a ($\text{M}\text{?}{}_{\mathrm{n}}\text{? 1000}$). In the polymer melts (I) E_a values of free and bonded radicals first diminished as a consequence of the decrease of the end group effect and they achieved constant high molecular weight values (～15 and 25 kJ respectively). E_a changed in the solid state as a function of $\text{M}\text{?}{}_{\mathrm{n}}$ principally in the same manner except of the higher numerical values (～40 kJ).E_a of free and covalently bonded radicals in the transition region (II) gained a maximum at $\text{M}\text{?}{}_{\mathrm{n}}$ 1550 (125 and 170 kJ) and another at $\text{M}\text{?}{}_{\mathrm{n}}\text{> 9500}$ (130 and 165 kJ) expressing the high degree of order in these polymers in the solid state.The results obtained correlated well with the proton magnetic resonance measurements but they did not correlate with the amorphous dielectric relaxation measurements.It was concluded that the following factors may affect the rotational relaxations of nitroxyl radicals in PEG: the free volume of the polymer, the crystallinity, the chain packing and the end-group effect. The segmental character of the relaxation process was clearly indicated.     

Synthesis of electroreactive polymers from poly (m,p-chloromethylstyrene) and copoly (m,p-chloromethylstyrene-styrene)

Polymerization, and copolymerization with styrene, of m,p-chloromethylstyrene have been carried out at 75°C, in chlorobenzene and in the presence of AIBN ($\text{[}\text{AIBN}\text{] ? 6 × 10}{}^{\mathrm{?2}}$, and $\text{12 × 10}{}^{\mathrm{?2}}\text{m}$, respectively). The polymer molecular weights, determined by g.p.c., are: $\text{M}\text{?}{}_{\mathrm{w}}\text{= 8670}$, $\text{M}\text{?}{}_{\mathrm{n}}\text{= 5860}$, and $\text{M}\text{?}{}_{\mathrm{w}}\text{/-M}{}_{\mathrm{n}}\text{= 1.48}$ for the homopolymer, poly(m,p-chloromethylstyrene), (1a); and $\text{M}\text{?}{}_{\mathrm{w}}\text{= 8805}$, $\text{M}\text{?}{}_{\mathrm{n}}\text{= 5144}$, and $\text{M}\text{?}{}_{\mathrm{w}}\text{/-M}{}_{\mathrm{n}}\text{= 1.71}$ for the copolymer, copoly(m,p-chloromethylstyrene-styrene), (2a). A series of phosphine derivatives of both 1a and 2a are prepared by the reaction of the polymers with either chlorodiphenylphosphine/lithium, or diphenylphosphine/potassium tert. butoxide. A number of other potentially electroreactive derivatives of 2a are obtained by reacting the polymer with 2-aminoanthraquinone, 3-N-methylamino-propionitrile, or 2-(2-aminoethyl) pyridine. The phosphinated polymers are reacted with bis-benzonitrilepalladium-(II) chloride to obtain a series of polymer-palladium(II) complexes containing 8.5–12.9% palladium. Similarly, reaction of the last-named bidentate polymeric ligand with cupric acetylacetonate, or cupric sulphate pentahydrate, produces polymer-copper(II) complexes having 5.8, or 3.3% copper, respectively. The inter/intra-chain nature of some of the side reactions during the derivatization of the chloromethylated polymers, and that of the complex formation between transition metal centres and macromolecular ligands, are briefly discussed in view of the experimental results.     

Self-diffusion of poly(ethylene oxide) in aqueous dextran solutions measured using FT-pulsed field gradient n.m.r.

Transport in ternary polymer₁, polymer₂, solvent systems has been investigated using an n.m.r. spin-echo technique. The dependence of the self-diffusion coefficient of poly(ethylene oxide) polymers on the concentration and molecular size of dextran in aqueous solution has been measured. Monodisperse poly(ethylene oxide) fractions ($\text{M}\text{?}{}_{\mathrm{w}}\text{=7.3×10}{}^4$, 2.8·10⁵ and 1.2·10⁶) and dextrans ($\text{M}\text{?}{}_{\mathrm{w}}\text{=2·10}{}^4$, 1·10⁵ and 5·10⁵) have been employed over a range of concentration up to the miscibility limit in each system. It is found that when the molecular size of the diffusant is commensurate with or exceeds that of the matrix polymer, a relationship of the form: $\text{(}\text{D}\text{D}{}_0\text{)}{}_{\mathrm{<mtext>PEO</mtext>}}\text{=}\text{exp}\text{?k(C[η])}$ is applicable, where C[η] refers to the dextran component and is considered to describe the extent of coil overlap in concentrated solution. ($\text{D}\text{D}{}_0$) is independent of the molecular size of the poly(ethylene oxide), at least in the range studied (M_w<300 000).     

Copoly(m,p-chloromethylstyrene-50% styrene): Copolymer molecular weights,fractionation and derivatization

Copolymerization of an equimolar mixture of m,p-chloromethylstyrene ($\text{M}$₁) and styrene ($\text{M}$₂) was carried out in chlorobenzene in the presence of AIBN at 80°C. Molecular weight analysis (by g.p.c.) of the resulting polymer samples was performed at various conversions. $\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}$, $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$, and ($\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$) value of 21 300, 13 800 and 1.54 were obtained at 8.9% conversion. At higher conversions, the value of $\text{M}\text{?}{}_{\mathrm{<mtext>w</mtext>}}$ remained effectively constant while $\text{M}\text{?}{}_{\mathrm{<mtext>n</mtext>}}$ decreased to 9200 at ca. 80% conversion, and then increased to 12 000 at about 100% conversion (16 h), and to 13 700 if the polymer solutions were maintained at 80°C for an additional 44 h. These results suggest that, although the termination step initially involves the combination of polymer radicals, at high conversions a large number of very low molecular weight, and unsaturated, polymer molecules are formed possibly by disproportionation involving polymer radicals and primary radicals. The unsaturated polymer molecules are subsequently polymerized by growing polymer radicals towards the end of the polymerization. It was noticed that further reaction occurred after complete depletion of monomer, involving radical attack on the unsaturated polymer molecules. Other reactions including chain transfer to polymer will also be important at high polymer concentrations. A copolymer of $\text{M}$₁ and $\text{M}$₂ was separated into four fractions on a preparative scale, and molecular weight analysis of the resulting polymer samples provided more evidence of the above interpretation. G.p.c. analysis of several derivatives of a copolymer of $\text{M}$₁ and $\text{M}$₂ showed that most molecular weights were much lower than that of the starting polymer. These results in some cases may reflect the chemical or dimensional changes introduced into the polymer molecules during derivatization.     

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.     

Pulsed n.m.r. of cis-polyisoprene: 1

Proton spin-spin (T₂), and spin-lattice (T₁) relaxation time measurements are reported for six monodisperse cis-polyisoprenes ($\text{M}\text{?}{}_{\mathrm{n}}$ from 2000 to 200 000) over the temperature range from ?50° to 170°C. At low temperatures (?30° to 10°C) T₁ and T₂ are determined by the short range segmental motions but above 10°C T₂ is sensitive to the long range motions. When $\text{M}\text{?}{}_{\mathrm{n}}\text{? 30 000 T}{}_2$ becomes influenced by the presence of entanglements which produce a transient network structure and this confers on the spin-spin relaxation a pseudo-solid-like response. Similar behaviour is observed in crosslinked networks produced by irradiation. The results are discussed in terms of the types of motion occurring in amorphous polymers above T_g and the analogy with dynamic mechanical measurements is discussed.     

Studies of cyclic and linear poly(dimethyl siloxanes). 4. Bulk viscosities

The bulk viscosities η of over fifty sharp fractions of cyclic and linear poly(dimethyl siloxanes) in the weight-average molecular weight range $\text{500 <}\text{M}\text{?}{}_2\text{< 25 000}$ have been measured at 298 K using a cone- and-plate microviscometer. In the Iow molecular weight region $\text{M}\text{?}{}_{\mathrm{W}}\text{< 1000}$) the η values for the cyclics were found to be at least three times as large as the values for the corresponding chain molecules. By contrast, in the highest molecular weight region ($\text{M}\text{?}{}_{\mathrm{W}}\text{> 16 000}$), the η values for the cyclics were approximately one-half those for the corresponding linears. Cyclics and linears containing about one hundred skeletal bonds were found to have similar bulk viscosities. The temperature dependence of the bulk viscosities of eighteen of the cyclic and linear fractions were investigated, and the relationship $\text{η = A}\text{exp}\text{(}\text{E}{}_{\mathrm{<mtext>visc</mtext>}}\text{RT}\text{)}$ was used to deduce values for the energies of activation for viscous flow E_visc and the constants A.     

Cyclization dynamics of polymers: 9. The effect of polymer concentration on the slowest internal relaxation mode of a labelled polystyrene chain

A combination of steady-state and fluorescence decay techniques permits one to measure the dynamics of end-to-end cyclization of a polymer chain substituted at both ends with pyrene groups. In the limit of low concentration, the rate constant for cyclization, k_cy, can be identified with the slowest relaxation rate $\text{τ}{}_1{}^{\mathrm{?1}}$ of a Rouse—Zimm chain. Experiments are reported which allow k_cy to be examined for two chain lengths of polystyrene substituted on both ends with pyrene groups. These chains have $\text{M}\text{?}{}_{\mathrm{n}}\text{= 9200}$ and 25 000 ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{? 1.15}$). Added unlabelled polystyrene polymer [PS] causes $\text{k}\text{?}{}_{\mathrm{<mtext>cy</mtext>}}$ to decrease in cyclohexane just above the θ-temperature, whereas in toluene, a good solvent, k_cy is largely unaffected, even at [PS] concentrations of 50 wt%. These results are explained in terms of frictional effects—hydrodynamic screening—dominating in the poor solvent, whereas other factors tend to have offsetting effects in the good solvent.     

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.     

Differences in the molecular weight and the temperature dependences of self-diffusion and zero shear viscosity in linear polyethylene and hydrogenated polybutadiene

Within the context of a generalized coupling model we can support the hypothesis that, while the mode of relaxation for self diffusion (D) and shear flow (η) are the same, the entanglement interactions are different. We assume that there are two distinct coupling parameters n_D and n_η for self diffusion and shear flow respectively. The model predicts the molecular weight and temperature dependences to be scaled by the relevant coupling parameters as:

for melts with Arrhenius temperature dependences. We have found that n_n=0.43 and 0.42 for polyethylene (PE) and hydrogenated polybutadiene (HPB) which scale η as M^3.5 and M^3.4. Also the apparent flow activation energies $\text{E1}{}_{\mathrm{a}}$ of 6.35 kcal mole^?1 for PE and 7.2 kcal mol^?1 for HPB scale to primitive activation energies E_a of 3.6 and 4.2 kcal mole^?1 for PE and HPB respectively. On the other hand the M^?2 dependence of D results in n_D=1/3. Then the reported activation energies for self-diffusion in PE and HPB of 5.49 and 6.2 kcal mole^?1 scale to primitive activation energies of 3.7 and 4.1 kcal mole^?1, respectively.     

The θ-behaviour of heterogeneous macromolecules

A polymer chain consisting of N_r segments with a repulsive interaction (binary cluster integral β_r) and N_a ? N_r segments with a stronger, attractive and pairwise saturable interaction (β_a), which is at the averaged θ-point N²_rβ_r + N²_aβ_a = 0 deviations from the predictions of the two parameter theory: $\text{α}{}^2{}_{\mathrm{<mtext>R</mtext>}}\text{? 1 ～ δz}{}_{\mathrm{<mtext>r</mtext>}}\text{< 0}$ and A₂ ～ δz_r > 0 with $\text{δz}{}_{\mathrm{<mtext>r</mtext>}}\text{～ β}{}_{\mathrm{<mtext>r</mtext>}}\text{(}\text{N}{}_{\mathrm{<mtext>a</mtext>}}\text{N}{}_{\mathrm{<mtext>r</mtext>}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. It is shown that the deviations from the universal behaviour are due to the existence of an intermediate length scale $\text{～}\text{N}{}_{\mathrm{<mtext>a</mtext>}}\text{N}{}_{\mathrm{<mtext>r</mtext>}}$.     

Studies of cyclic and linear poly(dimethyl siloxanes): 2. Preparative gel permeation chromatography

A preparative gel permeation chromatographic (g.p.c.) instrument has been constructed and used to separate broad fractions of cyclic poly(dimethyl siloxanes) into sharp fractions with heterogeneity indices $\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{= 1.05 ± 0.02}$. The number-average molecular weights $\text{M}\text{?}{}_{\mathrm{n}}$ of the cyclic polymer fractions obtained were as high as 50 000, corresponding to number-average numbers of skeletal bonds $\text{n}\text{?}{}_{\mathrm{n}}$ up to 1300. The concentrations of linear poly(dimethyl siloxanes) in all but the highest molecular weight cyclic polymer fractions prepared are believed to be negligible. The preparative g.p.c. instrument was also used to obtain some sharp fractions of linear poly(dimethyl siloxanes).     

Properties of extremely high molecular weight polystyrene in solution

Extremely high molecular weight polystyrenes with a $\text{M}\text{?}{}_{\mathrm{w}}$ in the range 10.8 × 10⁶ to 2.2 × 10⁷ were prepared by emulsion polymerization initiated with a heterogeneous initiator at 30°C, which has a ‘living character’. Samples of polystyrene were characterized by light scattering and viscometry in toluene and benzene at 25°C, and in θ-solvent cyclohexane at 34.8°C. Also determined were the relationships of mean-square radius of gyration 〈s²〉 (m²) and the second virial coefficient A₂ (m³ mol kg^?2) on the molecular weight, which for toluene and benzene are described in equations: Toluene (25°C) $\text{〈s}{}^2\text{〉=1.59 × 10}{}^{\mathrm{?23}}\text{M}\text{?}{}_{\mathrm{w}}{}^{1.23}$; $\text{A}{}_2\text{=4.79 × 10}{}^{\mathrm{?3}}\text{M}\text{?}{}_{\mathrm{w}}{}^{\mathrm{?0.63}}$; Benzene (25°C) $\text{〈s}{}^2\text{〉=1.23 × 10}{}^{\mathrm{?22}}\text{M}\text{?}{}_{\mathrm{w}}{}^{1.20}$; $\text{A}{}_2\text{=2.59 × 10}{}^{\mathrm{?3}}\text{M}\text{?}{}_{\mathrm{w}}{}^{\mathrm{?0.59}}$. The parameters in the Mark-Houwink-Sakurada equation were established, for extremely high molecular weight polystyrene in toluene and in benzene, at 25°C into the form giving for $\text{[η] (}\text{m}{}^3\text{kg}{}^{\mathrm{?1}}\text{): [η] = 8.52 × 10}{}^{\mathrm{?5}}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.61}$; $\text{[η] = 1.47 × 10}{}^{\mathrm{?4}}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.56}$. The mentioned relations, as well as the obtained values of Flory parameter ?₀ and of ratio $\text{[η]}\text{M}\text{?}{}_{\mathrm{w}}{}^{0.5}$ were compared with solution properties of high molecular weight polystyrene with narrow molecular weight distribution prepared by anionic polymerization by Fukuda et al.     

Effect of molecular weight on the partial specific volume of polystyrenes in solution

The partial specific volume $\text{v}\text{?}{}_2$ of linear and branched polystyrenes has been measured as a function of molecular weight (1300<M_w<9×10⁶). In the low molecular weight range, the effect of end-groups is predominant. In the high molecular weight range (M_w > about 20 000), we have detected small but significant variations due to the intramolecular segment-segment contacts within the coil. We have proposed an empirical relation between $\text{v}\text{?}{}_2$ and the segment density of the macromolecule; this relation has been confirmed using highly branched polystyrenes. These results relative to dissolved polystyrenes are compared to experimental data obtained by different authors on pure liquid polystyrenes at different temperatures. Starting from simple additivity rules and from the known chemical composition of liquid polymers, we have shown that the variation of specific volume with high molecular weights is due to some phenomenon different from an effect of chain-ends.     

Determination of type and width of a size distribution from the z-averages of the radii moments rnz

Relationships are given between the z-average radii moments $\text{r}\text{?}{}^{\mathrm{n}}{}_{\mathrm{z}}$ and the common moments $\text{r}\text{?}{}^{\mathrm{n}}$ of a size distribution. Instructions are given for finding the type and width of a size distribution from measurements of the $\text{r}\text{?}{}^{\mathrm{n}}{}_{\mathrm{z}}$ moments.     

Assessment of the activities of catalysts for the hydrocracking of coal by means of hydrogen evolution

A close relation has been found between hydrogen evolution from coal-catalyst and pitch-catalyst systems and catalytic activities of liquefaction reactions. A MoO₃?TiO₂ catalyst has the highest activity and the order of activity of the catalysts for hydrogen evolution is: MoO₃?TiO₃> MoO₃?SiO₂>10% $\text{Fe}{}_2\text{O}{}_3\text{TiO}{}_2\text{?AI}{}_2\text{O}{}_3\text{>}\text{coal alone}$. The same trend was observed for benzene-soluble materials for the hydrocracking of Akabira Coal.     

Cyclization dynamics of polymers: 10 Synthesis,fractionation, and fluorescent spectroscopy of pyrene end-capped polystyrenes

The rate constant for end-to-end cyclization (k₁) for polymer chains is predicted to decrease sensitively with increasing chain length. In this paper the techniques are examined critically for extracting values of k₁ from experiments involving intramolecular pyrene excimer formation in polymers of the form pyrene-polystyrene-pyrene. For significance, results require samples of appropriately narrow molecular weight distribution ($\text{M}\text{?}{}_{\mathrm{w}}\text{M}\text{?}{}_{\mathrm{n}}\text{</ 1.13}$), as well as corrections for polydispersity differences among the samples. Particular attention is focussed both on experimental techniques and on the models used to interpret the kinetics of intramolecular pyrene excimer formation.