Kinetics of loop formation in polymer chains

We investigate the kinetics of loop formation in ideal flexible polymer chains (the Rouse model), and polymers in good and poor solvents. We show for the Rouse model, using a modification of the theory of Szabo, Schulten, and Schulten, that the time scale for cyclization is tau(c) approximately tau(0)N(2) (where tau(0) is a microscopic time scale and N is the number of monomers), provided the coupling between the relaxation dynamics of the end-to-end vector and the looping dynamics is taken into account. The resulting analytic expression fits the simulation results accurately when a, the capture radius for contact formation, exceeds b, the average distance between two connected beads. Simulations also show that when a < b, tau(c) approximately N(alpha)(tau), where 1.5 < alpha(tau) < or = 2 in the range 7 < N < 200 used in the simulations. By using a diffusion coefficient that is dependent on the length scales a and b (with a < b), which captures the two-stage mechanism by which looping occurs when a < b, we obtain an analytic expression for tauc that fits the simulation results well. The kinetics of contact formation between the ends of the chain are profoundly effected when interactions between monomers are taken into account. Remarkably, for N < 100, the values of tau(c) decrease by more than 2 orders of magnitude when the solvent quality changes from good to poor. Fits of the simulation data for tau(c) to a power law in N (tau(c) approximately N(alpha)(tau)) show that alpha(tau) varies from about 2.4 in a good solvent to about 1.0 in poor solvents. The effective exponent alpha(tau) decreases as the strength of the attractive monomer-monomer interactions increases. Loop formation in poor solvents, in which the polymer adopts dense, compact globular conformations, occurs by a reptation-like mechanism of the ends of the chain. The time for contact formation between beads that are interior to the chain in good solvents changes nonmonotonically as the loop length varies. In contrast, the variation in interior loop closure time is monotonic in poor solvents. The implications of our results for contact formation in polypeptide chains, RNA, and single-stranded DNA are briefly outlined.     

Elastic properties of poly(hydroxybutyrate) molecules

Elasticity of various poly(hydroxybutyrate) (PHB) molecules of regular and irregular conformational structure was examined by the molecular mechanics (MM) calculations. Force - distance functions and the Young's moduli E were computed by stretching of PHB molecules. Unwinding of the 2(1) helical conformation H is characterized at small deformations by the Young's modulus E = 1.8 GPa. The H form is transformed on stretching into the highly extended twisted form E, similar to the beta-structure observed earlier by X-ray fiber diffraction. The computations revealed that in contrast to paraffins, the planar all-trans structure of undeformed PHB is bent. Hence, a PHB molecule attains the maximum contour length in highly straightened, but slightly twisted conformations. A dependence of the single-chain moduli of regular and disordered conformations on the chain extension ratio x was found. The computed data were used to analyze elastic response of tie (bridging) molecules in the interlamellar (IL) region of a semi-crystalline PHB. A modification of the chain length distribution function of tie molecules tau(N) due to secondary crystallization of PHB was conjectured. The resulting narrow distribution tau(N) comprises the taut tie molecules of higher chain moduli prone to overstressing. The molecular model outlined is in line with the macroscopically observed increase in the modulus and brittleness of PHB with storage time.     

Conformational supramolecular isomerism in one-dimensional silver(I) coordination polymer of a flexible bis(bidentate) N,N-donor ligand with p-xylyl spacer

The isolation and structural characterisation of three isomeric silver(I) complexes, 1a, 1b and 2 with the general formula {[AgL(1)]ClO(4)}(n) (where L(1) is a bis(bidentate) N,N-donor ligand derived from the Schiff-base condensation of α,α'-diamino-p-xylene and pyridine-2-carboxaldehyde) are discussed. Single-crystal X-ray structures reveal the polymeric nature for the complexes where all the silver ions are in pseudotetrahedral geometry with the AgN(4) coordination environment. Isomers 1a (Pc space group) and 1b (Cc space group) were crystallised from acetonitrile whereas 2 (C2/c space group) was crystallised during the synthesis from a solvent mixture of dicholormethane and methanol. The flexible ligand (L(1)) adopts only an anti conformation in 1b and the presence of two different anti conformations in the repeating unit results in the formation of a trapezoidal wave polymeric chain. However, both gauche and anti conformations of the ligand are found to be present in the polymeric chains of 1a. In the polymeric chain of 2, only one anti isomer of the ligand is present in the repeating unit resulting in a triangular wave chain. The structure of isomer 1a is solvent induced and solvent plays a major role in the crystal packing of this isomer. One-dimensional coordination polymers 1a, 1b and 2 are related to each other as conformational supramolecular isomers. Additionally, two independent polymeric chains parallel to each other: one triangular wave consisting of only an anti conformation and a trapezoidal wave chain consisting of alternate gauche and anti conformations of the ligand are observed in 1a. This is a rare example of two supramolecular isomers present in the same crystal. Six different conformers of the flexible ligand are observed in the crystals of coordination polymers.     

Polymer translocation through a nanopore under an applied external field

We investigate the dynamics of polymer translocation through a nanopore under an externally applied field using the two-dimensional fluctuating bond model with single-segment Monte Carlo moves. We concentrate on the influence of the field strength E, length of the chain N, and length of the pore L on forced translocation. As our main result, we find a crossover scaling for the translocation time tau with the chain length from tau approximately N2nu for relatively short polymers to tau approximately N1+nu for longer chains, where nu is the Flory exponent. We demonstrate that this crossover is due to the change in the dependence of the translocation velocity v on the chain length. For relatively short chains v approximately N-nu, which crosses over to v approximately N(-1) for long polymers. The reason for this is that with increasing N there is a high density of segments near the exit of the pore, which slows down the translocation process due to slow relaxation of the chain. For the case of a long nanopore for which R parallel, the radius of gyration Rg along the pore, is smaller than the pore length, we find no clear scaling of the translocation time with the chain length. For large N, however, the asymptotic scaling tau approximately N1+nu is recovered. In this regime, tau is almost independent of L. We have previously found that for a polymer, which is initially placed in the middle of the pore, there is a minimum in the escape time for R parallel approximately L. We show here that this minimum persists for weak fields E such that EL is less than some critical value, but vanishes for large values of EL.     

二维HP格点模型中的紧密高分子链构象及其热力学性质的研究

采用二维HP模型用精确计数法和MonteCarlo方法研究了链长为N(≤ 2 2 )的紧密高分子链的构象和热力学性质 .发现不同HP序列的紧密高分子链的平均自由能和平均配分函数与链长N存在关系 :〈F〉=aN+b ,　ln〈Z〉=a′N +b′ .同时发现对于可折叠成基态且简并度为 1的紧密高分子链 ,其平均自由能和平均配分函数与链长N也存在相似的关系 .在HP模型中对于链长为N的紧密高分子链 ,存在着 2 N + 1 个不同的HP序列 .我们发现可以折叠成基态且简并度为 1的蛋白质分子的HP序列数目NS 为NS =a× 2 N+ 1 　 (a =0 0 2 5 ) ,对应的HP序列中 ,疏水基团 (H)数目的含量为 4 0 %～ 6 0 %的序列出现的几率最大 .同时在这些紧密高分子链中有些具有相同的结构 ,发现结构的‘简并度’为 3 3～ 4 0 (10≤N≤ 16 ) .在紧密高分子链折叠过程中 ,折叠的初期能量下降比较快 ,折叠的中期能量下降比较缓慢 ,折叠的后期能量下降也是比较快     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

Understanding interactions between poly(styrene-co-sodium styrene sulfonate) and single-walled carbon nanotubes

Understanding formation mechanisms of hybrids of carbon nanotubes (CNTs) wrapped by polymers and their interactions is critical in modifying solubility of CNTs in aqueous solution and developing new nanotube-based polymer materials. In the present work, we investigate the structural details of poly(styrene-co-sodium styrene sulfonate) (PSS) wrapping around the CNT and the interactions between the PSS chain and the CNT using molecular dynamics (MD) simulations. The fraction of sulfonated groups significantly influences the wrapping conformations of the PSS chain. Due to limited time scale in the MD simulations, two different initial conformations of the chains are introduced to explore the effect of the initial state on the wrapping behavior. When the chains initially wrap around the CNT in a perfect helix manner, more compact pseudo-helical conformations are obtained. For initial straight line arrangement of the chain monomers, the chains adopt looser wrapping conformations. The free-energy analysis and binding interaction of the PSS chain on the CNT surface take a glance on the relationship between the conformational transition of the chain and the energy evolution.     

Scaling law of poly(ethylene oxide) chain permeation through a nanoporous wall

This paper presents a study of the permeation of poly(ethylene oxide) (PEO) chains through the nanoporous wall of hollow polymeric capsules prepared by self-assembly of polyelectrolytes. We employ the method of pulsed field gradient (PFG) NMR diffusion to distinguish chains in different sites, i.e., in the capsule interior and free chains in the dispersion, by their respective diffusion coefficient. From a variation of the observation time, the time scale of the molecular exchange between both sites and thus the permeation rate constant is extracted from a two-site exchange model. Permeation rate constants show two different regimes with a different dependence on chain length. This suggests a transition between two different mechanisms of permeation as the molecular weight is increased. In either regime, the permeation time can be described by a scaling law tau approximately N (b) , with b = (4)/ 3 for short chains and b = (1)/ 3 for long chains. We discuss these exponents, which clearly differ from the theoretical predictions for chain translocation.     

Conformational behavior of polymers adsorbed on nanotubes

The importance of hydrophobic interactions in determining polymer adsorption and wrapping of carbon nanotubes is still under debate. In this work, we concentrate on the effect of short-ranged weakly attractive hydrophobic interactions between polymers and nanotubes (modeled as an infinitely long and smooth cylindrical surface), neglecting all other interactions apart for chain flexibility. Using coarse-grained Monte Carlo simulation of such simplified systems, we find that uniform adsorption and wrapping of the nanotube occur for all degrees of chain flexibility for tubes with sufficiently large outer radii. However, the adsorbed conformations depend on chain stiffness, ranging from randomly adsorbed conformations of the flexible chain to perfect helical or multihelical conformations (in the case of more concentrated solutions) of the rigid chains. Adsorption appears to occur in a sequential manner, wrapping the nanotube nearly one monomer at a time from the point of contact. Once adsorbed, the chains travel on the surface of the cylinder, retaining their helical conformations for the semiflexible and rigid chains. Our findings may provide additional insight to experimentally observed ordered polymer wrapping of carbon nanotubes.     

Synthesis and esterolytic reactions of linear and cross-linked asymmetric imidazole-containing polymers

Asymmetric linear and cross-linked imidazole-containing polymers were prepared from 1-[2(S)-methylbutyl]-4-vinylimidazole and 1-[2(S)-methylbutyl]-5-vinylimidazole. The esterolytic reactions of these linear and cross-linked asymmetric polymers with the enantiomeric substrates (R)- and (S)-4-(3-methylpentadecanoyl)-3-nitrobenzoic acid, (R)- and (S)-S, were studied by measuring the pseudo-first order kinetics of the solvolysis of these enantiomeric substrates in the presence of these asymmetric polymers. The linear homopolymers and copolymers of 1-[2(S)-methylbutyl]-4- and 5-vinylimidazole showed hydrophobic and electrostatic effects in the solvolysis of the enantiomeric substrates with these linear asymmetric polymers. Cross-links were introduced into these asymmetric polymers to increase the rigidity and reduce the number of conformations available to the polymer. The reduced conformational mobility was expected to enhance any enantioselectivity in the solvolysis of the enantiomeric substrates with these polymers. Using these cross-linked polymers, hydrophobic interactions were observed in the solvolysis of a series of substrates with increasing alkyl chain length. Also, on changing the polarity of the solvent, a bell-shaped rate profile was observed in the solvolysis of the long chain substrate S. This effect was attributed to a combination of the coiling of the cross-linked polymer chains and hydrophobic interactions with the substrate on changing solvent polarity. Even with the increased rigidity of these cross-linked polymers, no significant enantioselectivity in the solvolysis of the enantiomeric substrates was observed. So, neither the linear nor the cross-linked asymmetric polyvinylimidazoles showed enantioselectivity in the solvolysis of these enantiomeric substrates. In this case, the hydrophobic interactions and the reduced conformational mobility through crosslinking were not strong enough to bring about enantioselectivity in the solvolysis of these enantiomeric substrates.     

Synthesis and molecular structures of two [1,4-bis(3-pyridyl)-2,3-diazo-1,3-butadiene]-dichloro-Zn(II) coordination polymers

Two novel coordination polymers with 3D metal-organic frameworks (MOFs) have been synthesized by reacting 1,4-bis(3-pyridyl)-2,3-diazo-1,3-butadiene (L) with zinc dichloride. Both compounds have the same repeating unit consisting of a distorted tetrahedral Zn(II) center coordinated by two chlorides and two pyridyl nitrogen atoms of two bridging bismonodentate L ligands, however, different structural conformations have been found, one forming a helical chain and the other producing a square-wave chain. The intermolecular C-H...Cl hydrogen bonds in 1 and 2 play important roles in the formation of three-dimensional coordination polymers. Compound 1 crystallized in an orthorhombic space group Pna21 with a = 7.9652(3), b = 21.4716(7), c = 8.2491(3)A, V = 1410.81(9) A 3 and Z = 4. Compound 2 crystallized in a monoclinic space group P21/n with a = 9.1752(3), b = 14.5976(4), c = 10.3666(3) A , beta = 98.231(2) degrees , V = 1374.16(7) A 3 and Z = 4.     

The role of molecular mechanics in the prediction of the chain conformation of polymers in the crystalline state: Syndiotactic polymers

Molecular mechanics methods have been used in order to find the conformations of various syndiotactic polymers in crystals. Three different classes of polymers have been examined: i) polyolefins, such as poly(propylene), polystyrene, poly(1‐butene) and poly(1,2‐butadiene); ii) polydienes, such as cis‐1,4‐poly(1,3‐pentadiene); iii) alternating copolymers of carbon monoxide with styrene or styrene derivatives. The presence of conformational polymorphism in some of the studied polymers is predicted and explained by maps and minimizations of the conformational energy. The calculated internal parameters and chain axis repeats of all the considered polymers result in very good agreement with X‐ray experimental data reported in literature. The role of intramolecular nonbonded interactions in determining the conformations of the polymer chains is thoroughly discussed.     

Stretching semiflexible polymer chains: evidence for the importance of excluded volume effects from Monte Carlo simulation

Semiflexible macromolecules in dilute solution under very good solvent conditions are modeled by self-avoiding walks on the simple cubic lattice (d = 3 dimensions) and square lattice (d = 2 dimensions), varying chain stiffness by an energy penalty ε(b) for chain bending. In the absence of excluded volume interactions, the persistence length l(p) of the polymers would then simply be l(p) = l(b)(2d - 2)(-1)q(b) (-1) with q(b) = exp(-ε(b)/k(B)T), the bond length l(b) being the lattice spacing, and k(B)T is the thermal energy. Using Monte Carlo simulations applying the pruned-enriched Rosenbluth method (PERM), both q(b) and the chain length N are varied over a wide range (0.005 ≤ q(b) ≤ 1, N ≤ 50,000), and also a stretching force f is applied to one chain end (fixing the other end at the origin). In the absence of this force, in d = 2 a single crossover from rod-like behavior (for contour lengths less than l(p)) to swollen coils occurs, invalidating the Kratky-Porod model, while in d = 3 a double crossover occurs, from rods to Gaussian coils (as implied by the Kratky-Porod model) and then to coils that are swollen due to the excluded volume interaction. If the stretching force is applied, excluded volume interactions matter for the force versus extension relation irrespective of chain stiffness in d = 2, while theories based on the Kratky-Porod model are found to work in d = 3 for stiff chains in an intermediate regime of chain extensions. While for q(b) ? 1 in this model a persistence length can be estimated from the initial decay of bond-orientational correlations, it is argued that this is not possible for more complex wormlike chains (e.g., bottle-brush polymers). Consequences for the proper interpretation of experiments are briefly discussed.     

Disulfide bond isomerization in basic pancreatic trypsin inhibitor: multisite chemical exchange quantified by CPMG relaxation dispersion and chemical shift modeling

Conformational changes occurring on the microsecond-millisecond time scale in basic pancreatic trypsin inhibitor (BPTI) are investigated using nuclear magnetic resonance spectroscopy. The rczz CPMG experiment (Wang, C.; Grey, M. J.; Palmer, A. G. J. Biomol. NMR 2001, 21, 361-366) is used to record (15)N spin relaxation dispersion data, R(ex)(1/tau(cp)), in which 1/tau(cp) is the pulsing rate in the CPMG sequence, at two static magnetic fields, 11.7 and 14.1 T, and three temperatures, 280, 290, and 300 K. These data are used to characterize the kinetics and mechanism of chemical exchange line broadening of the backbone (15)N spins of Cys 14, Lys 15, Cys 38, and Arg 39 in BPTI. Line broadening is found to result from two processes: the previously identified isomerization of the Cys 38 side chain between chi(1) rotamers (Otting, G.; Liepinsh, E.; Wüthrich, K. Biochemistry 1993, 32, 3571-3582) and a previously uncharacterized process on a faster time scale. At 300 K, both processes contribute significantly to the relaxation dispersion for Cys 14 and an analytical expression for a linear three-site exchange model is used to analyze the data. At 280 K, isomerization of the Cys 38 side chain is negligibly slow and the faster process dominates the relaxation dispersion for all four spins. Global analysis of the temperature and static field dependence of R(ex)(1/tau(cp)) for Cys 14 and Lys 15 is used to determine the activation parameters and chemical shift changes for the previously uncharacterized chemical exchange process. Through an analysis of a database of chemical shifts, (15)N chemical shift changes for Cys 14 and Lys 15 are interpreted to result from a chi(1) rotamer transition of Cys 14 that converts the Cys 14-Cys 38 disulfide bond between right- and left-handed conformations. At 290 K, isomerization of Cys 14 occurs with a forward and reverse rate constant of 35 s(-1) and 2500 s(-1), respectively, a time scale more than 30-fold faster than the Cys 38 chi(1) isomerization. A comparison of the kinetics and thermodynamics for the transitions between the two alternative Cys 14-Cys 38 conformations highlights the factors that affect the contribution of disulfide bonds to protein stability.     

Polymer translocation through a nanopore. II. Excluded volume effect

Following our previous study of a Gaussian chain translocation, we have investigated the transport of a self-avoiding chain from one sphere to another sphere through a narrow pore, using the self-consistent field theory formalism. The free energy landscape for polymer translocation is significantly modified by excluded volume interactions among monomers. The free energy barrier for the placement of one of the chain ends at the pore depends on the chain length N nonmonotonically, in contrast to the N-independence for Gaussian chains. This results in a nonmonotonic dependence of the average arrival time [tau0] on N for self-avoiding chains. When the polymer chain is partitioned between the donor and recipient spheres, a local free energy minimum develops, depending on the strength w of the excluded volume interaction and the relative sizes of the donor and recipient spheres. If the sizes of spheres are comparable, the average translocation time tau (the average time taken by the polymer, after the arrival at the pore, to convert from the donor to the recipient) increases with an increase in w for a fixed N value. On the other hand, for the highly asymmetric sizes of the donor and recipient spheres, tau decreases with an increase in w. As in the case of Gaussian chains, tau depends nonmonotonically on the pore length.     

Excluded volume effects on the intrachain reaction kinetics

On the basis of the recently developed optimized Rouse-Zimm theory of chain polymers with excluded volume interactions, we calculate the long-time first-order rate constant k(1) for end-to-end cyclization of linear chain polymers. We first find that the optimized Rouse-Zimm theory provides the longest chain relaxation times tau(1) of excluded volume chains that are in excellent agreement with the available Brownian dynamics simulation results. In the free-draining limit, the cyclization rate is diffusion-controlled and k(1) is inversely proportional to tau(1), and the k(1) values calculated using the Wilemski-Fixman rate theory are in good agreement with Brownian dynamics simulation results. However, when hydrodynamic interactions are included, noticeable deviations are found. The main sources of errors are fluctuating hydrodynamic interaction and correlation hole effects as well as the non-Markovian reaction dynamic effect. The physical natures of these factors are discussed, and estimates for the magnitudes of required corrections are given. When the corrections are included, the present theory allows the prediction of accurate k(1) values for the cyclization of finite-length chains in good solvents as well as the correct scaling exponent in the long-chain limit.     

Unexpected relaxation dynamics of a self-avoiding polymer in cylindrical confinement

We report extensive simulations of the relaxation dynamics of a self-avoiding polymer confined inside a cylindrical pore. In particular, we concentrate on examining how confinement influences the scaling behavior of the global relaxation time of the chain, tau, with the chain length N and pore diameter D. An earlier scaling analysis based on the de Gennes blob picture led to tau approximately N(2)D(13). Our numerical effort that combines molecular dynamics and Monte Carlo simulations, however, consistently produces different tau results for N up to 2000. We argue that the previous scaling prediction is only asymptotically valid in the limit N"D(53)"1, which is currently inaccessible to computer simulations and, more interestingly, is also difficult to reach in experiments. Our results are thus relevant for the interpretation of recent experiments with DNA in nano- and microchannels.     

Dynamical scaling of single chains on adsorbing substrates: diffusion processes

We study the dynamics of tethered chains of length N on adsorbing surfaces, considering the dilute case; for this we use the bond fluctuation model and scaling concepts. In particular, we focus on the mean-square displacement of single monomers and of the center of mass of the chains. The characteristic time tau of the fluctuations of a free chain in a good solvent grows as tau approximately N(a), where the coefficient a obeys a=2nu+1. We show that the same coefficient also holds at the critical point of adsorption. At intermediate time scales single monomers show subdiffusive behavior; this concurs with the behavior calculated from scaling arguments based on the dynamical exponent a. In the adsorbed state tau(perpendicular), the time scale for the relaxation in the direction perpendicular to the surface, becomes independent of N; tau(perpendicular) is then the relaxation time of an adsorption blob. In the direction parallel to the surface the motion is similar to that of a two-dimensional chain and is controlled by a time scale given by tau(parallel) approximately N(2nu(2)+1)L(-2Delta(nu/nu)), where nu(2) is the Flory exponent in two dimensions, nu is the Flory exponent in three dimensions, and Deltanu=nu(2)-nu. For the motion parallel to the surface we find dynamical scaling over a range of about four decades in time.     

Miscibility behavior and single chain properties in polymer blends: a bond fluctuation model study

Computer simulation studies on the miscibility behavior and single chain properties in binary polymer blends are reviewed. We consider blends of various architectures in order to identify important architectural parameters on a coarse grained level and study their qualitative consequences for the miscibility behavior. The phase diagram, the relation between the exchange chemical potential and the composition, and the intermolecular pair correlation functions for symmetric blends of linear chains, blends of cyclic polymers, blends with an asymmetry in cohesive energies, blends with different chain lengths, blends with distinct monomer shapes, and blends with a stiffness disparity between the components are discussed. For strictly symmetric blends the Flory‐Huggins theory becomes quantitatively correct in the long chain length limit, when the χ parameter is identified via the intermolecular pair correlation function. For small chain lengths composition fluctuations are important. They manifest themselves in 3D Ising behavior at the critical point and an upward parabolic curvature of the χ parameter from small‐angle neutron scattering close to the critical point. The ratio between the mean field estimate and the true critical temperature decreases like √χ/(ρb³) for long chain lengths. The chain conformations in the minority phase of a symmetric blend shrink as to reduce the number of energeticaly unfavorable interactions. Scaling arguments, detailed self‐consistent field calculations and Monte Carlo simulations of chains with up to 512 effective segments agree that the conformational changes decrease around the critical point like 1/√N. Other mechanisms for a composition dependence of the single chain conformations in asymmetric blends are discussed. If the constituents of the blends have non‐additive monomer shapes, one has a large positive chain‐length‐independent entropic contribution to the χ parameter. In this case the blend phase separates upon heating at a lower critical solution temperature. Upon increasing the chain length the critical temperature approaches a finite value from above. For blends with a stiffness disparity an entropic contribution of the χ parameter of the order 10^–3 is measured with high accuracy. Also the enthalpic contribution increases, because a back folding of the stiffer component is suppressed and the stiffer chains possess more intermolecular contacts. Two aspects of the single chain dynamics in blends are discussed: (a) The dynamics of short non‐entangled chains in a binary blend are studied via dynamic Monte Carlo simulations. There is hardly any coupling between the chain dynamics and the thermodynamic state of the mixture. Above the critical temperatures both the translational diffusion and the relaxation of the chain conformations are independent of the temperature. (b) Irreversible reactions of a small fraction of reactive polymers at a strongly segregated interface in a symmetric binary polymer blend are investigated. End‐functionalized homopolymers of different species react at the interface instantaneously and irreversibly to form diblock copolymers. The initial reaction rate for small reactant concentrations is time dependent and larger than expected from theory. At later times there is a depletion of the reactive chains at the interface and the reaction is determined by the flux of the chains to the interface. Pertinent off‐lattice simulations and analytical theories are briefly discussed.     

Structure and conformation of DAB dendrimers in solution via multidimensional NMR techniques.

NOESY-HSQC 3D-NMR and NOESY 2D-NMR techniques have been used on a 750 MHz spectrometer to study the chain conformations of different generation DAB dendrimers (poly[propylene imine] dendrimers) in chloroform and benzene solutions. The high-field multidimensional NMR techniques provided the chemical shift dispersion needed to resolve all of the unique resonances in the dendrimers. By studying the NOE interactions among dendritic chain protons, information about through space interactions between protons on different parts of the dendrimer chain is obtained, which is directly related to the conformation of the dendrimer. These experiments also give further proof of the chemical shift assignments obtained from the HMQC-TOCSY 2D and 3D NMR experiments. The concentration effects on chemical shifts have also been observed, revealing information about the interactions between solvent and different parts of dendrimer molecules. These studies clearly show for DAB dendrimers, that folded chain conformations can occur in nonpolar solvents such as benzene and extended chain conformations are predominant in polar solvents such as chloroform.