Number Of Chain Segments Research Articles

Study of the Dynamic Viscoelasticity of Single Poly(N-isopropylacrylamide) Chains Using Atomic Force Microscopy

Thermoresponsive poly(N-isopropylacrylamide) (PNIPAM) is of great interest in the fields of medicine and pharmacology because its lower critical solubility temperature (LCST) is close to the physiological temperature. The understanding of the phase transfer mechanism of PNIPAM near the LCST is of great significance for the design, development, and application of its derivatives. In this study, a dynamic single-molecule force spectroscopy (SMFS) approach was used to quantitatively assess the dynamic viscoelasticity of single PNIPAM chains at different temperatures. We found that the relationship between the viscoelasticity coefficient of a single polymer chain in the low elongation region and the number of chain segments below the LCST was in accordance with the prediction of the Kirkwood model. Above the LCST, the PNIPAM chains exhibited different viscoelastic behaviors that were determined by their conformations. Importantly, the characterization of dynamic viscoelasticity allowed us to observe the phase transition behavior of single polymer chains in the low elongation region where they are similar to random coils, which helped us to understand the microscopic mechanism of their temperature response. In particular, above the LCST, the PNIPAM chains no longer underwent purely entropic elastic behavior but instead displayed enthalpic viscoelastic behavior dominated by intramolecular hydrogen bonds.

An efficient algorithm for multiscale flow simulation of dilute polymeric solutions using bead-spring chains

In this study, a computationally efficient algorithm for multiscale flow simulation of dilute polymer solutions using a bead-spring chain description of polymer molecules is presented. The algorithm combines a computationally efficient extension of the earlier BCF-based semi-implicit method (i.e., approximately four-fold speed up) for multiscale flow simulations using a bead-spring dumbbell description [M. Somasi, B. Khomami, Linear stability and dynamics of viscoelastic flows using time-dependent stochastic simulation techniques, J. Non-Newtonian Fluid Mech. 93 (2000) 339–362] with a highly CPU efficient predictor–corrector scheme for BD simulation of bead-spring chains [M. Somasi, B. Khomami, N. Woo, J. Hur, E. Shaqfeh, Brownian dynamics simulations of bead-rod and bead-spring chains: numerical algorithms and coarse-graining issues, J. Non-Newtonian Fluid Mech. 108 (2002) 227–255]. The fidelity and computational efficiency of the parallel implementation of the algorithm are demonstrated via three benchmark flow problems, namely, plane Couette flow, Poiseuille flow and 4:1:4 axisymmetric contraction–expansion flow. The algorithm shows linear speed up with the number of processors and more importantly with the number of chain segments. In addition, the proposed algorithm is approximately 50 times faster in comparison to the only existing fully implicit method [J. Ramirez, M. Laso, Size reduction methods for the implicit time-dependent simulation of micro-macro viscoelastic flow problems, J. Non-Newtonian Fluid Mech. 127 (2005) 41–49].

Monolayer Model Simulations of Mixtures of Amphiphilic Molecules

AbstractAthermal Monte Carlo simulations for a mixed monolayer built up from flexible molecules with different chain lengths have been carried out within a cubic lattice model. Only excluded volume interactions are taken into account. The number of chain segments per molecule, the head density, and the mole fraction of each component are varied. It is the aim of the work to investigate the orientational order in such mixtures. The calculated correlation lengths and snapshots did not show any evidence for demixing. In order to understand the effect of mixing on ordering some additional properties of the system have been investigated. Results demonstrating the influence of the mole fraction and chain length on the orientational order parameter, the end‐end distance, the end‐end projection, and the density profiles are presented. These quantities exhibit deviations from an ideal mixing rule. The deviations get stronger with increasing relative chain length difference. The shorter chains do not align in the local environment of long chains.

Motion of a polyelectrolyte chain hooked around a post.

The release kinetics of a single DNA molecule hooked around an obstacle in the presence of an electric field is investigated. A kinetic model which includes both electrical and stretching forces is introduced and used both in computer simulation and in the development of a simple analytic argument. These predict two regimes which depend on \ensuremath{\Upsilon}=N/\ensuremath{\beta}, where N is the number of chain segments and 1/\ensuremath{\beta} is the dimensionless field strength. For short chains, \ensuremath{\Upsilon}1, the characteristic unhooking time scales as ${\mathit{N}}^{2}$, whereas for long chains, \ensuremath{\Upsilon}\ensuremath{\gtrsim}1, it scales as N. Without introducing post friction, the model is able to reproduce recent experimental observations.

Deuterium NMR of Strained Swollen Crossunked Elastomers: Effect of Crosslink Density on the Orientational Order of Chain Segments

Abstract The 2H NMR of uniaxially strained swollen chloroprene rubbers and butadiene-styrene copolymers with different crosslink densities is studied. the relative number of chain segments between cross-links of various samples is obtained. the results are in approximate agreement with those obtained from the Flory equilibrium-swelling method. It is found that the enhancement factor G depends not only on the lattice-walk model and swelling of rubber, such as Tanaka etc. expected, but also on the crosslink density and the structure of the rubber. the formula relating G to the number of chain segments between cross links is derived from theory. Moreover, we can also estimate the relation between the enhancement factor Gr of real rubber and G calculated from the theory of the lattice model. the 2H NMR results of these samples indicate that the interaction between chain segments decreases with increasing crosslink density.

Fracture Energy and Critical Strength of High Molecular Weight Glassy Polymers

ABSTRACTThe fracture energy and the critical strength of glassy polymers with molecular weight larger than the critical value for the onset of chain entanglements are proportional to the number of chain segments entangled about a unit plane. A new molecular model is presented to calculate the crossing density of these chain segments when the segment length is a stochastic variable. The crossing density depends on the mesh size of the entanglement network and the number of entanglement network strands per unit volume. Theoretical predictions of the variation of the fracture energy and strength with the molecular weight are compared with experimental results for various glassy polymers.

The spans of a polyelectrolyte near a charged surface

The mean spans of a polyelectrolyte strongly adsorbed on a charged surface are calculated. The spans in the directions parallel to the surface depend only on the number of chain segments while the span in the direction perpendicular to the surface depends only on the Debye screening length and the surface–segment interaction energy.

An explanation of switching characteristics in polymer ferroelectrics by a nucleation and growth theory

In polymer ferroelectrics, the change of polarization under an applied field is known to occur by formation of kinks or twists of polarization and by propagation of solitary waves along individual chain axes. Measurements of the switching characteristics in β-phase poly(vinylidene fluoride), β-PVDF, and in copolymers of vinylidene fluoride and trifluoroethylene have shown that the switching times of these polymers vary exponentially with the reciprocal of applied field. This exponential dependence can be explained adequately by a random domain nucleation and growth model rather than by a continuous process of twist propagation as suggested by Clark and Taylor. In addition, the nucleation and growth model is found to be consistent with the observed exponential dependence of switching time on temperature. The formation of a critical nucleus requires the realignment of polarizations of several neighboring chain segments which is accomplished by propagation of kinks along individual chain axes. The number of chain segments in the critical nucleus depends on the applied field and temperature, and. in the case of β-PVDF, it is estimated to be in the range of 6 to 23 at the applied field of 100 MV/m and at room temperature.

The incipient characteristic tearing energy for an elastomer crosslinked under strain

AbstractIn a previous paper a two‐network model for an elastomer in which crosslinks have been introduced in the strained state, similar to that proposed by Green and Tobolsky, was used to calculate the dependence of the incipient characteristic tearing energy on the number of chain segments in each of the two networks, the number of links in these chain segments, and the deformation at which the crosslinking takes place. The tearing energies were calculated for tearing on planes perpendicular to the principal directions of this deformation. Here the calculations are extended to cover tearing on a plane with arbitrary orientation.

Attempt to correlate the formation of free volume and the plastic deformation process in glassy polymers

Both the formation of free volume and the elementary motion characterizing the plastic deformation in the glassy state are described here by the same molecular process, consisting of the transition of a given number of chain segments from fundamental to activated states. Using this basic assumption, a model is proposed which makes use of classical laws of thermodynamics. Five parameters need to be adjusted to take into account the thermodynamic properties related to the free volume: one more is necessary to characterize the molecular process of plastic deformation. The pressure dependence of T g and the difference between the specific volumes found in the glassy state from isothermal and isobaric measurements can be calculated from the model. Fairly good agreement is found between the theoretical and experimental values of these quantities. The physical meaning of constants belonging to a previously-proposed yield criterion is clarified, and these constants are given as a function of the molecular process. Moreover, the treatment confirms that the glass transition temperature is related to a constant fraction of activated segments and not to a constant value of the free volume.

Some general features of [formula omitted] relations for oligomers and amorphous polymers

The glass transition temperatures for a number of oligomers and polymers have been measured as a function of chain length. Analysis of these results, in conjunction with similar published data, has revealed that a plot of Tg against log x (where x is the number of chain segments) can be divided into three distinct regions. These are: Region I where the asymptotic value of Tg has been reached. Region II where Tg becomes chain length dependent and Region III in which the substance is still in its oligomeric form and Tg is even more chain length dependent. The boundary conditions defining the limits of these regions are embodied in the equations Tg(∝) = 372·6 log x c − 59.5, which is the boundary between Regions I and II Tg(∝) = 761·5 log x 0 − 681·8, which delineates the oligomeric and polymeric Regions III and II. These relations allow one to estimate at what molecular weight the limiting value of Tg is achieved for a given polymer and where the oligomer polymer transition zone is likely to occur.

Relaxation characteristics and intrinsic birefringence and viscosity of polystyrene solutions for a wide range of molecular weights

AbstractA comparison is made between measurements on polystyrene solutions and the relaxation characteristics and intrinsic birefringence and viscosity given by the theory for the flexible Gaussian chain of variable number of segments and with internal viscosity and internal hydrodynamic interaction. This is done in order to determine the applicability of the theory to polymers over a wide range of molecular weights, including the low molecular weight range in which there may be conflict with the theoretical assumption of chains having a large number of segments. The longest, terminal relaxation time and the number of chain segments are determined from measurements of the frequency dependence of oscillatory flow birefringence while the intrinsic birefringence and viscosity are determined from steady flow measurements. The range of molecular weights studied is from approximately 900 at 106. It is found that the segment weight is approximately 1000 and the number of segments is in direct proportion to the molecular weight for the range from 1 to 1000 segments. The terminal relaxation time has a molecular weight dependence of the type given by the theory but with better agreement for higher molecular weights. While the measured dependences of the intrinsic viscosity and birefringence are in agreement with theory for molecular weights greater than 5 × 104, they deviate significantly for molecular weights below 1 × 104. The ratio of the intrinsic birefringence to intrinsic viscosity, which in theory is a constant independent of molecular weight, is found to change at the lower molecular weights.

Viscosity, Sedimentation, et Cetera, of Ring- and Straight-Chain Polymers in Dilute Solution

The hydrodynamic properties of straight-chain and ring-chain polymers whose dimensions are expanded over those of similar Gaussian coils have been calculated by a perturbation method based on the normal-coordinate treatment with hydrodynamic interaction. Expansion is characterized by a parameter ε, such that the mean-square length is proportional to N1+ε, N being the number of chain segments. For straight chains the intrinsic viscosity, expressed in terms of the Flory Φ (×10−23), decreases from 2.81 at ε=0 to 0.686 at ε=0.5, while for rings Φ varies from 1.85 to 0.422; the ratio straight:ring increases slowly from 1.5 to 2.0. The sedimentation coefficient of the straight chain increases by a factor of 2.4 over this range of ε, while that of the ring goes up 2.2-fold. The ratio straight: ring rises slowly from 0.85 to 0.91. The results on straight chains agree with those of previous workers, and the straight:ring ratio agrees with several experiments on the sedimentation of straight and ring forms of various DNA's. It is apparent that viscosity should be a much more sensitive measure of ring formation than sedimentation, and that the effect of ring formation is roughly the same regardless of chain expansion (i.e., the same both in Gaussian coils and in a stiff chain such as DNA).

Viscoelasticity of Rubber

Abstract A theory has been obtained for the viscoelastic behavior of rubber in the frequency range above that at which creep is important and below that at which it behaves like a hard solid. The rubber chains are treated as springs in a viscous medium, and a general expression is obtained for the contribution to modulus of a single section of chain as a function of its length and terminations. A statistical estimate is made of the number of chain segments having given length and terminations. A modulus function is found for the group of chains with each kind of termination, and these are added in the proper amounts to give the form of the modulus vs. frequency curve for any amount of cross-linking. Measurements of shear modulus were made on one apparatus at frequencies between 0.0125 and 750 cps. Agreement is good if a pure viscosity is added to the theory. However, at low frequencies the imaginary part of modulus does not decrease as much as predicted.