Kinetics of the Coil−Globule Transition of Poly(methyl methacrylate) in a Mixed Solvent

Coil-globule transition in two-dimensional polymer chains in an explicit solvent

The structure of two-dimensional polymer chains in a solvent at different temperatures is still far from being fully understood. Computer simulations of high-density macromolecular systems require the use of appropriate algorithms, and therefore the simulations were carried out using the Cooperative Motion Algorithm. The polymer model studied was exactly two-dimensional, coarse-grained and based on a triangular lattice. The theta temperature and temperature of coil-to-globule transition, and critical exponents were determined. The differences between the structure of such a disk and that of a chain in a dense polymer liquid were shown.

Slow knot formation by suppressed self-reptation in a collapsed polymer chain

Chain-expansion processes from knotted globules have been measured for poly(methyl methacrylate) (PMMA) in the mixed solvent tert-butyl alcohol (TBA) + water (2.5 vol %) by static light scattering. The solution was quenched from the Θ temperature of 41.5 °C to 37.0 °C, aged there for a time period t(p,) and then returned rapidly to the Θ temperature. The chain-expansion process was determined as a time evolution of the expansion factor α(2) after the temperature increase. The measurement was carried out by changing the aging time t(p) from 240 to 7200 min, and the molecular weight from M(w) = 4.0 × 10(6) to 1.5 × 10(7), by taking advantage of the extremely slow chain aggregation in the solution. The chain-expansion process obtained for M(w) = 1.22 × 10(7) became slow with increasing t(p), which revealed the knot formation in single globules. The characteristic time of the chain expansion from globules aged for t(p) = 7200 min was found to depend on the molecular weight as M(w)(2.7). This exponent, which is close to 3, demonstrated a disentanglement process due to self-reptation. The present data were compared with the previous data of the chain expansion from compact globules aged at 25.0 °C. The comparison made at M(w) = 1.22 × 10(7) and at the same values of t(p) revealed that the chain expansion from the globules aged at 25.0 °C was much faster than that from the globules at 37.0  °C, indicating a lower knot density in the more compact globules. It was conjectured that the knot formation due to self-reptation would be suppressed in a compact globule because an entire conformational change required by knot formation would become difficult to occur in the confined space of high segment concentration, particularly for a long polymer chain. The chain collapse of PMMA in the mixed solvent has been observed to occur extremely slowly at the later stage. This slow process was explained by the suppressed self-reptation.

Comparison of the kinetics of chain aggregation and chain collapse in dilute polymer solutions

The rates of chain aggregation of poly(methyl methacrylate) (PMMA) in acetonitrile (AcN) and in the mixed solvent of AcN+water (10 vol%) were determined by static light scattering and compared with the rates of chain collapse [Maki, J. Chem. Phys. 126, 134901 (2007)]. Dilute solutions of PMMA with the molecular weight m{w}=6.4 x 10{6} and in the concentration range of (0.8-5)x10;{-4}gcm;{3} were quenched below the cloud point, and the weight-average molecular weight M{w} and z -average square radius of gyration S;{2}_{z} for clusters of PMMA chains were measured as a function of the time t after the quench and the concentration c . The measurement of chain aggregation was carried out up to the cluster size of M{w}m{w} approximately 30 , which required time periods of hours to several days depending on the concentration and solvent. The chain aggregation in AcN+water occurred much faster than that in AcN. The growth of clusters in both the solvents was represented by the exponential function as M{w} approximately e;{gct} and S;{2}_{z} approximately e{hct} , where g and h represent the intrinsic rate of chain aggregation. The ratio sigma of the intrinsic rate in AcN+water to that in AcN was estimated to be 9 by taking a rough average of the ratios 9.4 obtained from g and 8.8 from h . This value is comparable to the ratio 11 of the rate of chain collapse of PMMA in AcN+water (10 vol%) to that in AcN. This close value of the ratios indicates that the nature of solvent would affect the rates of chain collapse and chain aggregation through a similar mechanism.

Transition from a chain-collapse process to a chain-aggregation process of poly(methyl methacrylate) in a mixed solvent

The transition from a chain-collapse process to a chain-aggregation process was studied by static light scattering on poly(methyl methacrylate) of the molecular weight mw=1.22x10(7) in the mixed solvent tert-butyl alcohol+water (2.5 vol%). The concentration c of the solutions ranged from 0.5 to 2.5x10(-4) g/cm3 and the measurement was carried out at appropriate time intervals up to the time t(h)=3250 after the quench to 35.0 degrees C which was a few degrees below the phase separation temperature. The molecular weight Mw and mean-square radius of gyration<s2>z were estimated from each scattering curve determined at the finite concentrations. At the initial stage of 100 h, <s2>z decreased rapidly with the time t indicating the chain collapse, while at the later stage of 3000 h, <s2>z increased very slowly indicating the chain aggregation. The chain-collapse process and chain-aggregation process could be analyzed separately, though the two processes overlapped appreciably at the higher concentrations. The former process depended slightly on the concentration, while the latter process showed the exponential growth of ln Mw approximately ct and ln<s2>z approximately ct. In the plot of ln<s2>z versus ln Mw, the chain-collapse process was depicted by different lines depending on the concentration, while the chain-aggregation process was described by a single straight line. The transition from the former to the latter process occurred distinctly near 200 h after the quench irrespective of the concentration.

Kinetics of chain collapse in dilute polymer solutions: Molecular weight and solvent dependences

The molecular weight and solvent dependences of the characteristic time of chain collapse were studied for poly(methyl methacrylate) (PMMA) of the molecular weight Mw=6.4x10(6) and 1.14x10(7) in pure acetonitrile (AcN) and in the mixed solvent of AcN+water (10 vol %). The size of PMMA chains was measured as a function of the time after the quench by static light scattering and the chain collapse processes were expressed by the plot of the expansion factor alpha2 vs ln t. The chain collapse in the mixed solvent AcN+water (10 vol %) was found to occur much faster than that in pure AcN, though the measurement of the former collapse process required several hours. In order to make a comparison between the rates of chain collapses, the fast chain collapse process was superposed on the slow one by scaling the time of the fast process as gammat. The scale factor gamma was determined by comparing the chain collapse processes of nearly the same equilibrium expansion factor with each other. Accordingly, the superposition of the collapse for Mw=6.4x10(6) on that for Mw=1.14x10(7) yielded gammam=4.0+/-0.6 for the process in AcN+water and 5.5+/-0.6 in AcN. The superposition of the chain collapse process in AcN+water on that in AcN yielded gammas=9.5+/-1.4 for Mw=6.4x10(6) and 12.0+/-1.8 for Mw=1.14x10(7). This analysis suggests that gammam and gammas are constant independent of each other. Thus, by assuming the molecular weight dependence of gammam approximately Mz, the characteristic time tauexp of chain collapse was conjectured as tauexp approximately kappaMz, where kappa reflects the nature of solvent species. The ratio of kappa for PMMA in AcN to that in AcN+water is given by gammas. The exponent was estimated to be z=2.4+/-0.7 for AcN+water and 3.0+/-0.7 for AcN. These values are compatible with the theoretical prediction z=3 based on a phenomenological model, though the observed characteristic times are longer by several orders of magnitude than those of the theoretical prediction.

Memory effect in the chain-collapse process in a dilute polymer solution

The effect of temperature perturbation on a single-chain-collapse process was studied for poly(methyl methacrylate) with the molecular weight M(w)=1.05 x 10(7) in the mixed solvent of tert-butyl alcohol+water (2.5 vol %). In the chain-collapse process after a quench from the theta; temperature to a temperature T(1), the temperature was changed from T(1) to T(2) at the time t(1) after the quench and returned to T(1) at the time t(1)+t(2). In the three stages at T(1), T(2), and T(1), measurements of the mean-square radius of gyration of polymer chains were carried out by static light scattering and the chain-collapse process was represented by the expansion factor as a function of time. An effect of chain aggregation on the measurements was negligibly small because of the very slow phase separation. For the negative temperature perturbation (T(1)>T(2)), the chain-collapse processes observed in the first and third stages were connected smoothly and agreed with the collapse process due to a single-stage quench to T(1). A memory of the chain collapse in the first stage at T(1) was found to persist into the third stage at the same temperature T(1) without being affected by the temperature perturbation of T(2) during t(2). The memory effect was observed irrespective of the time period of t(2). The positive temperature perturbation (T(1)<T(2)) showed an acceleration of the chain-collapse process.