For the analysis of phase-separation behavior of compressible polymer blends and block copolymer melts, an equation-of-state (EOS) model is combined with the compressible random-phase approximation (RPA) formalism. The EOS model to be employed is obtained from extending an off-lattice model, recently given for interpreting compression response of pure polymers to pressure by Cho and Sanchez (CS), to polymer blends. The free energy for the CS model consists of an ideal free energy of Gaussian chains and a nonideal free energy that represents the excluded volume effects and the attractive interactions in given blend systems. This nonideal free energy yields the RPA interaction fields, with which monomer-monomer correlation functions for polymer blends or block copolymers are calculated to determine the condition of phase separation. It is shown that the theory can predict not only macrophase separation in some polymer blends but also microphase separation in the corresponding block copolymer melts. Especially, microphase separation upon heating, recently observed in several diblock copolymer melts, is shown to be driven by finite compressibility in given copolymer systems. The stability of diblock copolymer melts exhibiting microphase separation upon heating is also discussed in relation to the symmetry of phase diagrams.

IMPORTANCE Modern digital platforms are easily accessible and intensely stimulating; it is unknown whether frequent use of digital media may be associated with symptoms of attention-deficit/hyperactivity disorder (ADHD).OBJECTIVE To determine whether the frequency of using digital media among 15-and 16-year-olds without significant ADHD symptoms is associated with subsequent occurrence of ADHD symptoms during a 24-month follow-up.DESIGN, SETTING, AND PARTICIPANTS Longitudinal cohort of students in 10 Los Angeles County, California, high schools recruited through convenience sampling. Baseline and 6-, 12-, 18-, and 24-month follow-up surveys were administered from September 2014 (10th grade) to December 2016 (12th grade). Of 4100 eligible students, 3051 10th-graders (74%) were surveyed at the baseline assessment.EXPOSURES Self-reported use of 14 different modern digital media activities at a high-frequency rate over the preceding week was defined as many times a day (yes/no) and was summed in a cumulative index (range, 0-14).MAIN OUTCOMES AND MEASURES Self-rated frequency of 18 ADHD symptoms (never/rare, sometimes, often, very often) in the 6 months preceding the survey. The total numbers of 9 inattentive symptoms (range, 0-9) and 9 hyperactive-impulsive symptoms (range, 0-9) that students rated as experiencing often or very often were calculated. Students who had reported experiencing often or very often 6 or more symptoms in either category were classified as being ADHD symptom-positive. RESULTS Among the 2587 adolescents (63% eligible students; 54.4% girls; mean [SD] age 15.5 years [0.5 years]) who did not have significant symptoms of ADHD at baseline, the median follow-up was 22.6 months (interquartile range [IQR], months). The mean (SD) number of baseline digital media activities used at a high-frequency rate was 3.62 (3.30); 1398 students (54.1%) indicated high frequency of checking social media (95% CI, 52.1%-56.0%), which was the most common media activity. High-frequency engagement in each additional digital media activity at baseline was associated with a significantly higher odds of having symptoms of ADHD across follow-ups (OR, 1.11; 95% CI, 1.06-1.16). This association persisted after covariate adjustment (OR, 1.10; 95% CI, 1.05-1.15). The 495 students who reported no high-frequency media use at baseline had a 4.6% mean rate of having ADHD symptoms across follow-ups vs 9.5% among the 114 who reported 7 high-frequency activities (difference; 4.9%; 95% CI, 2.5%-7.3%) and vs 10.5% among the 51 students who reported 14 high-frequency activities (difference, 5.9%; 95% CI, 2.6%-9.2%).CONCLUSIONS AND RELEVANCE Among adolescents followed up over 2 years, there was a statistically significant but modest association between higher frequency of digital media use and subsequent symptoms of ADHD. Further research is needed to determine whether this association is causal.

A new Monte Carlo simulation on a coarse-grained tetrahedral lattice was recently developed for rotational isomeric state polyethylene chains. The short-range interaction was included by extending the classical statistical weight matrix. To describe the cohesive nature of realistic polyethylene systems, nonbonded long-range interaction was considered. The second virial coefficient B 2 of two chains under an interparticle potential was suitably written in a discretized form to be analyzed for this new lattice. Utilizing the vanishing B 2 of a ϑ chain was previously suggested for the estimation of interaction parameters representing several nearest neighbors. This approach was shown to be sufficient for treatment of dilute solutions, where long-range interactions are relatively infrequent. This study presents an alternative method of parameter estimation which is more appropriate for the bulk state, where long-range interactions are abundant. Interaction parameters were defined from an averaging procedure of the Mayer function in the expression of B 2. In the latter method, the widely used Lennard-Jones potential and associated parameters for the monomeric unit were used to calculated the average Mayer function. The estimated interaction parameters were used to simulate the average neighbor occupancy and the nonbonded energy per monomer. The nonbonded energy showed a minimum when it was plotted as a function of density. The latter method is considered better for the estimation of long-range interaction and yielded the density of minimum energy in a physically reasonable range. The calculated cohesive energy was shown to be close to the range defined by experiment.

The effective interaction parameters, (χF) of the homologous series of deuterated polystyrene-block-poly(n-alkyl methacrylate) copolymers (dPS-b-PA n MA) from methyl (n = 1) to hexyl (n = 6) side groups have been investigated by small-angle neutron scattering and a Hartree (fluctuation correction) analysis. While χF for dPS-b-PA n MA with n = 1 and 6 is a typical decreasing function of temperature, it is shown that χF for n from 2 to 4 changes to a monotonic increase with temperature, revealing growing upward convexity. This action culminates in a maximum of χF for n = 5, which suggests an immiscibility loop-type behavior. Using the Hartree analysis for compressible diblock copolymers, the effect of directional interactions and the compressibility difference between the constituent blocks on χF is discussed. The ordering transition temperatures, their pressure dependences, and χF for the homologous block copolymer series are shown to be in good agreement with the experimental values.

The recently developed Hartree analysis for compressible diblock copolymers has been performed to study the thermodynamic origin of an immiscibility loop and its unprecedented pressure dependence observed in a diblock copolymer from polystyrene and poly(n-pentyl methacrylate). Certain specific interactions (SI) were incorporated in the theory by adding an entropic component into crosscontact interactions. An effective Flory-type interaction parameter χ cRPA, which carries not only the change in contact interactions but also compressibility difference between blocks, was shown to play a central role here. The χ cRPA plotted against temperature exhibited a loop character with a maximum because of the input SI. The effects of both fluctuations and compressibility difference were found through χcRPA to yield a loop phase diagram for the copolymer in a feasible temperature range along with the peculiar dependence of the loop on copolymer chain sizes and pressure. The resultant theoretical phase behavior was shown to be harmonious with the experimental observations for the copolymer.

A new Landau free energy is derived for diblock copolymers of incompatible pairs based on the recently developed compressible random-phase approximation analysis. Finite compressibility of each block is generally allowed. The inhomogeneity of each block density and free volume is analyzed in the weak segregation regime. Free volume inhomogeneity fluctuates in two ways: One represents compressibility difference between blocks and the other stands for the screening of unfavorable cross-contacts. It is shown from the Landau energy that a continuous transition, observed in a symmetric block copolymer either incompressible or with no compressibility difference, disappears provided that one block is more compressible. Microphase transitions and their pressure response of commonly used diblock copolymers are calculated and compared with experimental results. A Flory-type interaction parameter χcRPA, which is suggested from the effective second-order vertex function in the free energy, is shown to be useful, owing to its compressible nature in understanding the phase behavior of various copolymers.

A mean-field Landau free energy is formulated for a compressible diblock copolymer melt that microphase separates upon heating. Finite compressibility, which induces microphase separation in such a copolymer, is incorporated into the free energy through interaction fields for describing effective interactions between constituent polymers. The condition of microphase separation transition and equilibrium microphase morphologies are determined for the diblock copolymer of deuterated polystyrene and poly(vinyl methyl ether) as a model system exhibiting the thermally induced microphase separation. The Landau analysis reveals that microphase separation transition for the given copolymer is of first order in the entire region of composition. The phase diagram for the copolymer including classical microphase morphologies is shown to be apparently different from that for typical diblock copolymers exhibiting microphase separation upon cooling. In addition, the fluctuations of free volume are analyzed after microphase separation. Excess free volume is shown to be present in the domains of a more compressible component.

Recently, it was found that polymers follow the principle of temperature−pressure (T−P) superposition. This principle states the temperature insensitiveness of the shape of the configurational free energy. An analytical free energy for polymeric liquids is developed in the framework of the perturbation theory to provide a better understanding of the T−P superposition principle. The intermer potential is separated into the repulsive reference and the attractive perturbed parts. The hard sphere potential is taken as the repulsive reference. The attractive part of the Mie (p,6) potential is taken as the perturbation. The free energy for the reference system of hard chains is obtained from the integration of the hard chain equation of state from the Baxter−Chiew theory. The limiting case of the reference free energy at infinite dilution is derived from the direct evaluation of the configurational partition function. The average packing energy is added as a perturbation energy. The local packing in the nearest neighbor is taken into consideration by the packing energy. The formulated free energy gives a unique interpretation of the empirical T−P superposition principle. The shape of the free energy is shown to be dominantly determined by the packing energy, especially by its (Mie potential) exponents. Therefore, its shape is dominantly temperature insensitive, which is the essence of the T−P superposition principle. In addition, it is shown that the theoretical internal pressure evaluated at atmospheric pressure possesses a maximum at a moderate temperature. At this point, the repulsion in the system starts to dominate the attractive interaction. Some experimental support for this behavior was given in the recent investigations into the bulk data of various polymers. These two features of the model yield the excellent correlation between the experimental and the theoretical polymer bulk properties. Better performance in fitting volumetric data is obtained if a more repulsive potential (p > 12) than the Lennard−Jones potential (p = 12) is used as a choice of the general Mie potential. This procedure culminates in the prediction of the cohesive energy (CE) of linear polyethylene at room temperature. The model with the Mie (18,6) potential gives the calculated CE within the experimental range, whereas the model with the Lennard−Jones potential overestimates the CE.