Dimensions Of Polymer Chains Research Articles

Dynamic light scattering of dilute PVA-borax aqueous solutions

Poly(vinyl alcohol)-borate (PVA-borate) complexes in dilute aqueous solutions were investigated by dynamic light scattering (DLS). Two relaxation modes obtained, were scattering vector-q2 dependent and diffusive. The amplitude of slow mode was independent of borax concentration. In the very dilute PVA concentration regime ( [PVA] < 5 g/L), the PVA di-diol-borate complexation was dominated by intra-molecular reaction, and the fast mode correlation length ςf which corresponds to the polymer chain dimension increased rapidly with borax concentrations lower than 0.06 M, and reached an asymptote in the higher borax concentration regime. However, for a dilute PVA aqueous solution with higher PVA content (i.e., [PVA] = 9 g/L), both intra-and inter-molecular PVA di-diol-borate complexations might happen. The chain expansion and shrinkage of PVA-borate complex with increasing borax concentration was observed due to the balance between the electrostatic repulsion of the charged diol-borate complexes and the intra-molecular crosslink induced by the intra-molecular di-diol-borate complexation.

Effects of the molecular weight of molecular chains constituting the reaction medium on the thermal degradation of polyisobutylene

Non-volatile oligomers obtained by the thermal degradation of polyisobutylene were finely fractionated and the distribution of the functional groups of each fraction was characterized by a kinetic approach including the intermolecular hydrogen abstraction of primary and tertiary terminal macroradicals (R p· and R t·) and volatile small radicals (S·), followed by β scission. The observed value of the composition ratio [TTD]/[NTTD], which is related to the ratio of the competitive β scission rates of a secondary on-chain macroradical, increases monotonically with decreasing molecular weight ( M) of the fractions. This result shows clearly that the reactivity for β scission depends on the segmental motion of the reacting radicals. With respect to the composition ratio [ t-Bu]/[iPr], which is related to the concentration ratio [R p·]/[R t·], the observed value is roughly constant with M for M > M c, but decreases with decreasing M for M < M c, where M c corresponds approximately to the characteristic molecular weight for the entanglement of molten polymer. This ratio for M > M c decreases with decreasing average molecular weight of the molten polymer matrix, owing to an increase in the rate of diffusion-controlled termination. For M < M c, the value of the exponent a determined from the slope of the double logarithmic plots of [ t-Bu]/[iPr] against M is about 0.5 in all cases. This suggests that the hydrogen abstraction of S· depends on the chain dimension of unentangled polymer. It is confirmed from these results that the degradation reaction of all the polymer molecules in an homogenous reaction medium is entirely affected by the segmental motion and self-diffusional motion of the degrading polymers, and the effect of the chain dimension is observed only for unentangled polymer molecules during the degradation.

Infusion of Polymer into a Porous Glass Bead As Studied by Space-Resolved Jamin Interferometry

Jamin interferometry was applied to a porous glass bead in order to observe transient infusion of solvated polymer into the medium after the polymer was added to the surrounding solvent. Analysis of the fringe pattern along the equator of the bead image allowed us to obtain the concentration profile of the polymer at different times during the infusion. It was found that there are some polymer chains that quickly enter the pores and spread throughout the medium. Afterward, the concentration profile slowly approached an equilibrium uniform distribution. When the polymer chain's dimension was smaller than the pore size, the approach was limited by intrapore diffusion of the chains. In contrast, the entrance of polymer chains into the pores near the bead surface was rate-limiting for polymer chains with a dimension larger than the pore size. The rate of entrance increased at higher concentrations. Unlike studies of transport through a porous membrane, space-resolved interferometry of the porous glass has the...

Dimensions of Polymer Chains in Critical Semidilute Solutions

In this Letter we present first measurements of the radius of gyration $({R}_{g})$ for polystyrene in deuterocyclohexane at the critical concentration of the polymer over a temperature range $\ensuremath{\Theta}\ensuremath{\ge}T\ensuremath{\ge}{T}^{c}$ using small-angle neutron scattering and the high-concentration labeling methodology. We do not observe a reduction of ${R}_{g}({T}^{c})$ at the critical temperature of phase demixing ${T}^{c}$ as compared to ${R}_{g}(\ensuremath{\Theta})$ in the $\ensuremath{\Theta}$ region, which indicates that the critical polymer solution cannot be considered as an ensemble of partially collapsed noninterpenetrating coils.

Shapes and motions of polysaccharide chains

Abstract

Fractal Brownian motion and polymers in external fields

Polymer behavior in external fields is modeled using fractal Brownian motion. The chain dimensions of polymer chains with and without excluded volume show a contour length dependence of Nv where v=h−1. Chains with excluded volume have h=3/5, chains without excluded volume, Gaussian chains have h=1/2, and for chains in the collapsed state h=1/3. This nonphysical result points to the distinction between fractals as models of the trajectory or path of a polymer that are self-similar on all length scales and real polymers that possess a lower and upper limit for self-similarity.

Conformational Characteristics and Unperturbed Chain Dimensions of the Oxygen-Containing Polymers [−OCH2CR2CH2−]n with R = H, CH3, and CH2CH3

MM3 molecular mechanics calculations reveal that poly(3,3‘-diethyloxetane) (PDEO) differs sharply from poly(3,3‘-dimethyloxetane) (PDMO) and poly(trimethylene oxide) (POM3) in terms of conformational preferences, notwithstanding the similarity of these three polymers as successive members of the homologous series [OCH2CR2CH2]n where R = CH2CH3, CH3, and H, respectively. Within the four-bond repeat unit OCH2CR2CH2, POM3 and PDMO both prefer ttgg while PDEO prefers tttt. These conformational differences are reflected in the predicted values of the characteristic ratio CR = 〈r2〉0/nl2 for the unperturbed chain dimensions (after allowance for the oxygen gauche effect) obtained from rotational-isomeric-state (RIS) calculations: 3.9 for POM3, 4.7 for PDMO, and 23 for PDEO. These CR values for POM3 and PDMO are consistent with experiment (3.9 and 4.3, respectively) and with previous theoretical treatments. The larger R substituent of PDEO compared with PDMO and POM3 imposes steric demands that offset the otherwise strong preference of the C−C backbone bonds for gauche states. This reversal in preference from gauche to trans causes the abrupt increase in CR since now the almost exclusively all-trans backbone of PDEO lacks the distinctive conformational randomness of POM3 and PDMO. In terms of Eσ = Et − Eg for the focal C−C bond in these polymers, comparison of the MM2, MM3, and Discover (plus a variant Discover‘) force fields reveals a wide disparity of values for Eσ and more so for the constituent energy components Estretch, Ebend, Etorsion, EvdW, and Eelectrostatics. The preference of the focal C−C bond in PDEO for trans over gauche involves a surprising degree of interplay among these energy components; hence the conformational analysis of PDEO would represent a stringent test of any existing or prospective force field.

Mark−Houwink−Kuhn−Sakurada Exponent at the ϑ Condition. Its Invariancy with Respect to the Cross-Sectional Dimensions of Polymer Chains

The question raised by Fujita has been examined, namely why the intrinsic viscosity of many polymers at the Θ condition [η] 0 is proportional to M 1/2 over a broad range of molecular weights. An explanation is proposed, based on a combination of the theory of the wormlike cylinder model with reported data on cross-sectional dimensions of 30 polymers with the carbon backbone differing in both the size and type of side groups (vinyl polymers, polyacrylates, polymethacrylates). The behaviors of poly(dimethylsiloxane) and poly(ethylene oxide), which are not in line with this explanation, are briefly discussed.

Composition‐dependent Flory‐Huggins parameters: molecular weight influences at high concentrations

AbstractFlory‐Huggins interaction parameters χ were determined by means of equilibrium vapor pressures (measured via a combination of a head‐space sampler with a gas chromatograph) and light scattering as a function of composition and temperature for the systems cyclohexanone/polystyrene [CHO/PS] and cyclohexanone/poly(butyl methacrylate) [CHO/PBMA]. The investigation of molecular weight influences on χ with the system CHO/PBMA demonstrates that they persist almost up to the pure polymer. In order to rationalize this result, it is postulated (in accord with experimental findings and theoretical predictions) that the dimensions of polymer chains may vary upon the addition of solvent even in highly concentrated solutions. From the information concerning χ(T) the inter action parameters were split into their enthalpy and entropy part. In the case of CHO/PS these quantities vary considerably with composition and turn out to be linearly interrelated.

Characterization of poly(methyl methacrylate)- graft-polystyrene prepared from methacryloyloxyethyl polystyrene macromonomer

Poly(methyl methacrylate)- graft-polystyrene was prepared by radical copolymerization of methyl methacrylate and methacryloyloxyethyl polystyrene macromonomer. By means of 1H n.m.r. spectroscopy and static light scattering (SLS), molecular weight distribution ( MWD) and chemical composition distribution ( CCD) were investigated for as-polymerized samples and their fractions separated by size exclusion. All fractionated samples had approximately the same chemical composition as those of the unfractionated copolymers. Apparent molecular weight measured by SLS was dependent upon solvent. The following conclusions were deduced from these results: the as-polymerized copolymers had polydispersities in CCD and MWD that were not correlated with each other. In contrast with the as-polymerized samples, the size-exclusion-fractionated samples showed a strong CCD-MWD correlation, while the two-dimensional distribution functions of CCD and MWD for all fractions were similar to each other. In view of the fact that the chain dimension of a long-branched polymer decreases with increasing branch density at the same molecular weight, the present results were consistently explicable.

Connection between Polymer Molecular Weight, Density, Chain Dimensions, and Melt Viscoelastic Properties

Models of a wide range of ethylene-butene copolymers have been made by the saturation of polybutadienes with a range of vinyl content. The viscoelastic of these polymers have been measured very precisely and their chain dimensions have been determined by SANS. To a high degree of correlation, it is found that the mean square unperturbed end-to-end distance 0 , the density ρ and molecular weight M are related to the plabteau modulus, G 0 , G N 0 ∞ { 0 ρ/M} 3 , a finding in accord with that of Ronca

The Application of Small Angle Neutron Scattering to Elastomers

Abstract The last twenty years have seen a dramatic increase in the application of small angle neutron scattering to polymer science. In this review the use of SANS to study elastomers and elastomeric systems has been summarized. This has focused on those applications most significant to the understanding of rubber. These have included the dimensions of polymer chains in the bulk melt state, the miscibility of polymer blends, the structure of block copolymers, and the nature of crosslinked networks. The information that has been obtained so far has cleared up many of the outstanding questions about elastomers, and one can only expect that this use will increase in the future and will yield a wealth of useful information.

Light‐Scattering evidence of a “critical” concentration for polymer coil shrinking in dilute solution

AbstractThe variation of polymer chain dimension with concentration in both dilute and extremely dilute solutions was monitored by measuring the diffusivity of narrowly distributed poly‐styrene standards in toluene at room temperature through a carefully designed dynamic light scattering experiment. As polystyrene concentration decreases, the measured translational diffusion coefficient levels off after a certain concentration, i.e., in terms of experimental results, there exists a “critical” concentration for polystyrene coil shrinking in dilute toluene solution. The existence of this critical concentration has been predicted by introducing the concept of screening length into the statistical thermodynamic calculation. In this paper, we report, for the first time, its laser light‐scattering evidence. © 1994 John Wiley &amp; Sons, Inc.

Small-angle neutron scattering studies of inhomogeneities in latex particles from emulsion homopolymerizations

Small-angle neutron scattering experiments were carried out to examine the extent of monomer/ polymer spatial inhomogeneities in latex particles formed in an emulsion homopolymerization, using contrast variation and isotopic labeling systems to look at the morphology of swollen and two-stage latices. Samples covered a range of molecular weights including systems where the radius of gyration of the polymer chains was both comparable to and smaller than the particle size. The experiments were designed to test separately inhomogeneities arising from two different effects: (1) the (thermodynamic) effect arising from the decrease in entropy of a polymer chain confined near the of a particle (the experiments here examined polymer distribution in polystyrene particles swollen with toluene); (2) surface (largely kinetic) arising mainly because, with a water-soluble initiator, free radicals enter latex particles at the (here experiments examined the distribution of newly formed polymer in seeded growth; related to this are inhomogeneities arising from finite rates of diffusion of monomer and of polymer). Results support the conclusion that repulsive wall effects do not give rise to significant nonuniformities but that inhomogeneities may arise in the final product where the polymer chain dimensions are substantially less than the particle radius. The latter conclusion is consistent with predictions of the anchoring model.

Effects of variable excluded volume on the dimensions of off-lattice polymer chains

The expansion of bead-stick models of polymer chains by excluded volume has been obtained by Monte Carlo methods for chains with ratios d of hard-sphere bead diameter to stick length between zero (no excluded volume) and unity (connected beads touching) for chains of from 9 to 99 beads. Values of mean-square end-to-end lengh and apparent power-law exponents 2ν= ∂ ln /∂ ln(N-1) for chains of N beads, for eight values of d from 0.30 to 0.93. For the range of chain lengths reported here, the apparent power-law exponent 2ν is not independent of d but rather shows a smooth, gradual transition from the well-known result for d= 0 to the previously reported value for d= 1

Studies on Polymer Chain Dimension in Solution——Calculation of Osmotic Pressures of Polymer Solutions

Studies on Polymer Chain Dimension in Solution——Calculation of Osmotic Pressures of Polymer Solutions

Unperturbed chain dimensions of polysilane in the third-order interaction approximation

The configurational energies, the characteristic ratio and the temperature coefficient for a polysilane chain with the third-order interaction are calculated. The characteristic ratios (〈 R 2〉/ nl 2) ∞ and (〈 S 2〉 0/ nl 2) ∞ are 3.57 and 0.575, respectively, and the temperature coefficient is −3.0 × 10 −3 deg −1. These results are less than those in the second-order interaction approximation. The third-order interaction approximation are useful for calculating the dimensions of polymer chains.

Dimensions of model polymer chains with variable excluded volume

Premiminary values of the exponent 2ν = d[ln ]/d[ln(N-1)] for the power-law dependence of mean-square end-to-end length (or other mean-square chain dimensions) upon the number N-1 of steps in the chain are obtained by least-squares fits of ln to linear functions of ln(N-1) for chains of from 9 to 99 beads. The results show that the apparent exponent 2ν increases smoothly with bead diameteras d increases from 0 to 1

Conformational characteristics of some model polydienes and polyolefins

The unperturbed chain dimensions of monodisperse polymers based on 1,3-butadiene, 2,3-dimethylbutadiene, 2-ethyl-1,3-butadiene and 3-methylene-7-methyl-1,6-octadiene and their saturated polyolefinic analogues were evaluated under θ or near-θ conditions via intrinsic viscosity measurements. Information was obtained regarding the influence of side-chain length on chain dimensions as well as the influence of head-to-head structures in polypropylene.

Chain dimensions in plastically deformed semicrystalline polymers

AbstractThe effect of plastic deformation on the chain dimensions of polymers in the semicrystalline state was investigated using linear hydrogenated polybutadiene (HPB), a model ethylene/butene‐1 copolymer having about 40% crystallinity at room temperature. Dilute blends of deuterium‐labeled chains with various molecular weights (20,000 ≤ M ≤ 214,000) in the same unlabeled matrix (M = 95,000) were uniaxially stretched at 25°C to extension ratios of α = 2.4 and 4.4. Radius of gyration normal to the stretch direction R⊥ was measured for the labeled chains by small‐angle neutron scattering. The molecular extension ratio inferred from these data αm = R/R was significantly smaller than α for short chains (M &lt; 50,000) but increased to the affine range αm = α for M &gt; 100,000. This variation in αm/α closely parallels the molecular weight dependence of mechanical strength and ductility in HPB over the same range.