Liquid crystalline polymers as additives to enhance the device properties of low molecular mass liquid crystals

Magnetic and electric fields have been used to determine the splay (k₁₁) and bend (k₃₃) elastic constants in a series of polymer/monomer liquid crystal solutions using the well known Freedericksz transition technique. Measurements have been carried out as a function of concentration and temperature. The polymer used was a smectogenic polysiloxane side chain liquid crystal with both cyanobiphenyl and benzoate ester side groups. The monomeric solvent was the nematogen 4-n-pentyl-4′-cyanobiphenyl. All of the solutions studied were nematogenic up to a concentration of 40% w/w. It has been shown that k₁₁, k₃₃ and $\text{k}{}_{33}\text{k}{}_{11}$ all decrease with increasing polymer concentration and that at high enough concentrations $\text{k}{}_{33}\text{k}{}_{11}$ tends to become independent of temperature. The implications of these results are discussed in terms of the performance of the most common liquid crystal display, i.e. the twisted nematic device.     

Molecular weight and temperature dependence of intrinsic viscosity of polymer solutions

The molecular weight and temperature dependence of the intrinsic viscosity of polymer solutions have been predicted by combining the calculated radius of gyration, R_G, and hydrodynamic radius, R_H, with either the static empirical approach of Mandelkern—Flory or the dynamic argument of Weill—des Cloizeaux. It is found that experimental results can be successfully represented by the dynamic model for a range of five decades of molecular weight and temperature. The discrepancy between the calculated and experimental data at $\text{N ? N}{}_{\mathrm{т}}$ reveals the crudeness of the discontinuity at the temperature cut-off assumed by current temperature blob theory.     

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.     

Cloud-point curves of the polystyrene-cyclohexane system near the critical point

Cloud-point curves for solutions of five polystyrene samples, including three well-fractionated polystyrenes, in cyclohexane have been examined near their critical points. Even for a solution of polystyrene characterized by $\text{M}{}_{\mathrm{w}}\text{M}{}_{\mathrm{n}}\text{<1.03}$, the critical point determined by the phase-volume method is generally situated on the right hand branch of the cloud-point curve. The precipitation threshold concentration is appreciably lower than the critical concentration, while the threshold temperature slightly deviates from the critical temperature. The agreement of the precipitation threshold point with the critical point has been found for a solution of polystyrene characterized by M_w=20×10⁴ and $\text{M}{}_{\mathrm{w}}\text{M}{}_{\mathrm{n}}\text{<1.02}$ in cyclohexane. The η(φ) function derived from critical miscibility data is expressed by $\text{χ(φ) = 0.2798+}\text{67.50}\text{T}\text{+0.3070φ+0.2589φ}{}^2$, which yields θ of 33.2°C and ψ₁ of 0.22.     

Molecular weight distributions in novolactype phenol-formaldehyde polymerization

To model the reversible novolac polymerization, five reactive species A to E have been defined. Molecules having bound CH₂OH (Q_n) are distinguished from those without it (P_n) and it is assumed that molecules of Q_n do not have more than one bound CH₂OH group. A kinetic model has been written and, based upon it, balance equations for molecules of novolac polymer in batch reactors have been derived. Based upon our earlier studies, the phenomenon of molecular shielding has been neglected. As a result, the reactivities of the ortho and para positions of phenol which are available in the literature could be used. The kinetic model for the molecular weight distribution (MWD) of reversible novolac polymer formation thus involves only one parameter. The study of the MWD of novolac polymer reveals two very important design variables: the phenol-formaldehyde ratio, $\text{[P]}{}_0\text{[F]}{}_0$, in the feed and the vacuum applied on the reactor. As the $\text{[P]}{}_0\text{[F]}{}_0$ ratio is increased, the breadth of the distribution is found to increase and it undergoes a maximum at $\text{[P]}{}_0\text{[F]}{}_0\text{? 1.4}$ for the set of rate constants chosen. At this ratio, the chain length average molecular weight is also found to be the largest. Industrially, the $\text{[P]}{}_0\text{[F]}{}_0$ ratio used in producing novolac polymer is 1.67 and it is usually desired that the polymer be linear with minimal branching. On application of vacuum, for a given time of polymerization, the chain length molecular weight is found to increase when the results are compared with those of batch reactors. The breadth of the distribution is also found to reduce thus giving a lower polydispersity index of the polymer formed.     

Polyelectrolyte behaviour of acrylonitrile methallylsulphonate copolymers in dimethylformamide

The properties in organic solvent (DMF) of two ionic copolymers are investigated and compared to those of polyelectrolytes in aqueous solutions. First, the viscometric behaviour is disccussed: it is demonstrated that [η] varies linearly with $\text{C}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}{}_{\mathrm{T}}$, where C_T is the ionic concentration of the solution. At infinite salt concentration we obtain data in agreement with unperturbed dimensions. Using isoionic dilution, we deduce ø_p, the osmotic coefficient. From osmometry, the dependence of ø_p on the concentration is obtained and compared to the theoretical value. In the presence of neutral salt, the osmotic pressure is determined as a function of salt and polymer concentrations. The results are interpreted in terms of a Donnan equilibrium.     

The dilute solution properties of maleic anhydride and maleic acid copolymers: 1. Light scattering, osmotic pressure and viscosity measurements

Dilute solution behaviour of poly(maleic anhydride-co-ethyl vinyl ether) and poly(maleic acid-co-ethyl vinyl ether) has been investigated by light scattering, osmotic pressure, and viscosity measurements. The molecular weights ($\text{M}\text{?}{}_{\mathrm{w}}$ and $\text{M}\text{?}{}_{\mathrm{n}}$), the second virial coefficients A₂, and the intrinsic viscosities [η] have been determined for three states of this copolymer: anhydride-form, H-form, and Na-salt independently. The constants in the Mark-Houwink relations were obtained for the above three states under different solvent conditions. The molecular weight of the anhydride-form is found to be higher than that of the acid-form or the Na-salt, suggesting the degradation in a process of hydrolysis. The second virial coefficient A₂ as well as the Mark-Houwink relation indicates that the anhydride-form and H-form behave as flexible polymer chains in good solvents. However, the polymer coil of Na-salt is highly expanded even at saturated NaCl concentration.     

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.     

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.     

The effect of a Gaussian distribution of chain-lengths on the phase-behaviour of a model system of rod-like macromolecules in solution

The calculations of Flory and co-workers for the formation and composition of isotropic, bi-phasic and anisotropic systems composed of rod-like macromolecules in solution have been extended to include a Gaussian distribution of rod-lengths. The critical concentrations for the beginning and end of the bi-phasic range $\text{v}{}^{\mathrm{<mtext>o</mtext><mtext>1</mtext>}}{}_{\mathrm{p}}$ and $\text{v}{}^{\mathrm{<mtext>o</mtext><mtext>7</mtext>}}{}_{\mathrm{p}}$ respectively, the volume fraction of anisotropic phase Φ_A, the compositions and average molecular weights of isotropic and anisotropic phases, and the order parameter S of the anisotropic phase are calculated as a function of polymer concentration v^o_p for rod-length x_o in the range 30 to 70 and for a Gaussian distribution half-width $\text{Δ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ in the range 10 to 70. The extent of the bi-phasic range and the composition of the two components is found to be strongly dependent on the breadth of the distribution and average rod-length. The applicability of the calculations to data for poly(alkylisocyanates) in solution is briefly considered.     

Flow microcalorimetry on dilute polymer solutions

A flow microcalorimeter designed to measure the heat of mixing of dilute polymer solutions is described. The instrument is sensitive to steady state heating rates of ～10 μJ/sec. Measurements of heats of mixing of solutions of differing concentrations of n-hexane and cyclohexane are reported and are compared with recommended data of McGlashan and Stoeckli. Values of:

$\text{K}{}_1\text{=}\text{lim}\text{V}{}_2\text{→ 0}$

$\text{(}\text{H}\text{?}{}_1\text{?}\text{H}\text{?}{}^0{}_1\text{RTv}{}^2{}_2$ are obtained for four polymer—solvent systems: polyisobutylene—benzene, 0.22; polystyrene (PS)—cyclohexane, 0.33; PS—n-butyl acetate, ?0.06 all at 25°C; and PS—toluene, ?0.05 at 40°C. Various theoretical calculations of second virial coefficients A₂ made with use of the calorimetric data are compared with previously measured A₂ for the first two mixtures.     

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 $\text{?W}\text{?I}{}_2$.     

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.     

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).     

Fluorescence probe for microenvironments: effect of solvent vapour on the properties of vapour-swollen polymers

The effect of solvent vapour on the properties of vapour-swollen vinyl chloride-vinyl acetate ($\text{83}\text{17}$) copolymer has been studied by a fluorescence probe, a p-N,N-dialkylaminobenzylidenemalononitrile derivative (1). Results show that the fluorescence quantum yield ($\text{Ф}{}_{\mathrm{<mtext>f</mtext>}}$) of 1 in vinyl chloride-vinyl acetate ($\text{83}\text{17}$) matrix decreases by a factor of ≈ 10, an indication of the increase in free volume or in polymer chain mobility, upon vapour swelling. The variations of $\text{Ф}{}_{\mathrm{<mtext>f</mtext>}}$ observed in various swollen matrices, which correlate only with the density of the swelling solvent, indicate that there is a profound vapour effect on the properties of swollen polymer. A density effect on the mobility of polymer chains in swollen polymer is proposed.     

The unperturbed molecular dimensions of poly(ethylene oxide) in aqueous solutions from intrinsic viscosity measurements and the evaluation of the theta temperature

Intrinsic viscosity measurements were carried out on five well characterized fractions of poly(ethylene oxide) in aqueous solutions at 24.9°, 34.9°, and 45.5°C. The Stockmayer-Fixman extrapolation was applied to the data: it yields the unperturbed dimensions K₀ of the chain. The unperturbed root-mean-square end-to-end distance $\text{〈}\text{R}\text{?}{}^2\text{〉}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}{}_0$ calculated for the polymer fractions in water indicate that the polymer molecules are expanded in this solvent as the temperature is raised. The temperature coefficient of unperturbed dimension, $\text{d In}\text{〈}\text{R}\text{?}{}^2\text{〉}{}_0\text{d}\text{t}\text{= 0.024}\text{K}{}^{\mathrm{?1}}$, calculated for poly(ethylene oxide) in water using the present data is about 100 times higher than the literature values of 0.23 (±0.02) × 10^?3 K^?1 and 0.2 (±0.2) × 10^?3 K^?1, respectively, obtained from force-temperature (‘thermoelastic’) measurements on elongated networks of the polymer in the amorphouse state and form viscosity measurements on this polymer in benzene. A value of θ=108.3°C was obtained from the temperature dependence of the interaction parameter B in the Stockmayer-Fixman equation.     

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.     

Rigid backbone polymers, XVII: Solution viscosity of polydisperse systems

When plotted against concentration V⁰₂, the viscosity η⁰ curve of isotropic solutions of lyotropic nematic mesomorphic polymers increases according to:

$\text{η}{}^0\text{=η}{}_0\text{[[η]V}{}^0{}_2\text{+(}\text{π}\text{4}\text{)[η]}{}^2\text{(V}{}^0{}_2\text{)}{}^2\text{+K}{}_2\text{(}\text{ln}\text{x}\text{)}{}^2\text{[η]}{}^3\text{(V}{}^0{}_2\text{)}{}^3\text{+…]}$

in which η₀ is the solvent viscosity, K₂ a numerical constant, x? is the average molecular axial ratio and [η] the intrinsic viscosity as defined by:

$\text{[η]=}\text{2}\text{x}{}^2\text{45}\text{1}\text{ln}\text{2}\text{x}\text{?1.84}\text{+}\text{3}\text{ln}\text{2}\text{x}\text{?0.61}\text{(+}\text{14}\text{15}\text{)}$

At the concentration $\text{v1}{}_2$ an anisotropic phase appears and the viscosity curve shows a decrease in slope followed by a change in direction at a peak viscosity η^p at v^p₂. Upon further increase in v⁰₂ the system undergoes a phase inversion and finally turns fully anisotropic at v^A₂. In the biphasic interval the viscosity is described by:

$\text{η}{}^0\text{=η}{}_{\mathrm{<mtext>mat</mtext>}}\text{1+}\text{(5λ+2)}\text{2(λ+1)}\text{V}{}_{\mathrm{<mtext>inc</mtext>}}$

where $\text{λ =}\text{η}{}_{\mathrm{<mtext>inc</mtext>}}\text{η}{}_{\mathrm{<mtext>mat</mtext>}}$, the ratio of the inclusions viscosity to the matrix viscosity, and v_inc the volume fraction of the inclusions in the system. It must be emphasized that the molecular weight of the polymer in both phases changes continuously with concentration, resulting in commensurate changes in η_ince, η_mat and their ratio λ. In the anisotropic region the viscosity first decreases moderately and then increases precipitously with v⁰₂, according to:

$\text{η}{}^0\text{=η}{}_0\text{[}\text{2}\text{x}{}^2\text{90S}\text{(}\text{5}\text{ln}\text{2}\text{x}\text{?1.8}\text{+}\text{6}\text{ln}\text{2}\text{x}\text{?0.61}\text{)+2]}\text{V}{}^0{}_2\text{1-}\text{V}{}_{\mathrm{25°}}\text{V}{}_{\mathrm{E}}$

in which S is an order parameter and V₂₅, V_E are volumes swept by the orbits of the flowing rodlike macromolecules. The equations give results in good qualitative and fair quantitative agreement with experimental data in the literature.