Abstract:Using a small-angle scattering technique, we measured the temperature dependence critical (multicritical) point is approached by a nonisomorphous path.
“…Accordingly, the critical index γ = 1.23 ± 0.02 for the susceptibility (i.e., the osmotic compressibility) in χ ∼ ( T − T C ) -γ at T ⇒ T C for all solutions studied agrees within experimental errors with the Ising model value (1.239 ± 0.002 12 ). The crossover takes place when ξ ∼ R g and thus reproduces the main features of the crossover observed in solutions of PS in CH- d (see the inset in Figure ). , These observations delineate an intrinsic analogy between the temperature behavior of polymers in SCFs and in liquid ϑ solvents in the vicinity of the UCST and show that polymer solutions in SCFs belong to the universality class of the Ising model. 1 ξ( T ) for h -PDMS with M W = 22 500 (▾), 47 700 (▴), and 79 900 (·).…”
Supercritical fluids (SCFs) have great technological potential for minimizing the organic
wastes associated with polymer manufacturing and processing. However, significant challenges remain
for developing the same level of understanding of the behavior of polymers in SCFs as has been reached
for polymers in traditional organic solvents. Small-angle neutron scattering was used to study the effect
of pressure and temperature on the phase behavior of poly(dimethylsiloxane) (PDMS) in supercritical
carbon dioxide (SC CO2). It was demonstrated that PDMS−SC CO2 solutions reproduce all main features
of the temperature−concentration phase diagram for polymers in organic solvents. Moreover, because of
their continuously adjustable solubility, SCFs exhibit novel effects, such as a pressure-induced transition
to the ϑ point and to the good solvent domain, in addition to a polymer−solvent demixing at a lower
critical solution pressure.
“…Accordingly, the critical index γ = 1.23 ± 0.02 for the susceptibility (i.e., the osmotic compressibility) in χ ∼ ( T − T C ) -γ at T ⇒ T C for all solutions studied agrees within experimental errors with the Ising model value (1.239 ± 0.002 12 ). The crossover takes place when ξ ∼ R g and thus reproduces the main features of the crossover observed in solutions of PS in CH- d (see the inset in Figure ). , These observations delineate an intrinsic analogy between the temperature behavior of polymers in SCFs and in liquid ϑ solvents in the vicinity of the UCST and show that polymer solutions in SCFs belong to the universality class of the Ising model. 1 ξ( T ) for h -PDMS with M W = 22 500 (▾), 47 700 (▴), and 79 900 (·).…”
Supercritical fluids (SCFs) have great technological potential for minimizing the organic
wastes associated with polymer manufacturing and processing. However, significant challenges remain
for developing the same level of understanding of the behavior of polymers in SCFs as has been reached
for polymers in traditional organic solvents. Small-angle neutron scattering was used to study the effect
of pressure and temperature on the phase behavior of poly(dimethylsiloxane) (PDMS) in supercritical
carbon dioxide (SC CO2). It was demonstrated that PDMS−SC CO2 solutions reproduce all main features
of the temperature−concentration phase diagram for polymers in organic solvents. Moreover, because of
their continuously adjustable solubility, SCFs exhibit novel effects, such as a pressure-induced transition
to the ϑ point and to the good solvent domain, in addition to a polymer−solvent demixing at a lower
critical solution pressure.
“…[3] in the mean field approximation which cannot reliably be used in the vicinity of the critical point. The distance between 0 and T c reflects the width of the crossover region from critical to tricritical.In our work [4] we have demonstrated that at the critical demixing point T c , polymer solutions must exhibit Ising-like critical behavior which is confirmed in [2]. The theory developed in [4] does not involve three-body interactions at the microscopic level; they appear, nevertheless, as fluctuation corrections to Flory-Huggins mean field theory [4,5].…”
supporting
confidence: 54%
“…(2) and (6) of [1] are taken from theories describing different critical regimes (e.g., see Ref. [2]): Equation (2) is valid in the tricritical region of the phase diagram (e.g., see Fig. 1 of [2]) while Eq.…”
mentioning
confidence: 99%
“…[2]): Equation (2) is valid in the tricritical region of the phase diagram (e.g., see Fig. 1 of [2]) while Eq. (6) is valid in the critical region.…”
mentioning
confidence: 99%
“…Moreover, by combining Eqs. (2) and (5) of [1] we can measure the cutoff directly and whence the persistence length [see, e.g., Eqs. (4.11) and (4.12) of [13]].…”
In a recent Letter [1] a direct measurement of the three-body interaction parameter was reported. The authors also have obtained the extrapolated values of 0(°°) and critical demixing T c (°°) temperatures which differ from each other. This difference was left unexplained in [1]. Here we would like to provide some explanation of the above difference.We begin with the observation that Eqs. (2) and (6) of [1] are taken from theories describing different critical regimes (e.g., see Ref. [2]): Equation (2) is valid in the tricritical region of the phase diagram (e.g., see Fig. 1 of [2]) while Eq. (6) is valid in the critical region. Moreover, Eq. (6) is obtained in Ref. [3] in the mean field approximation which cannot reliably be used in the vicinity of the critical point. The distance between 0 and T c reflects the width of the crossover region from critical to tricritical.In our work [4] we have demonstrated that at the critical demixing point T c , polymer solutions must exhibit Ising-like critical behavior which is confirmed in [2]. The theory developed in [4] does not involve three-body interactions at the microscopic level; they appear, nevertheless, as fluctuation corrections to Flory-Huggins mean field theory [4,5]. The role of microscopic three-body interactions in the critical region was discussed recently for the case of simple fluids in [6] and for the model lattice gas in [7]. In particular, in [7] the role of three-body interactions was studied nonperturbatively while in [3] these interactions were included perturbatively [which resulted in Eq. (6) of [1]] based on the earlier computational scheme of Ref. [8]. For the case of polymers, their nonperturbative role was emphasized in [9] while [4,5] provide some discussion of their importance in calculations of molecular weight dependencies of T C (M) and fluid diameter amplitude. In spite of the progress already achieved, some fundamental problems still remain to be solved (e.g., associated with field mixing [10]).We would also like to emphasize some aspects of Eq. (2) in [1], which are very important from the theoretical standpoint. Equation (2) can be obtained using Eqs. (2.3), (2.4), (7.13), and (7.17) of Ref. [11]. Unlike the previous calculation [12], where the dimensional regularization method was used, Ref.[11] employs the cutoff regularization so that Eq. (2) and Fig. 2(a) of [1] are direct manifestations of the importance of the cutoff methods in the tricritical theories. Moreover, by combining Eqs. (2) and (5) of [1] we can measure the cutoff directly and whence the persistence length [see, e.g., Eqs. (4.11) and (4.12) of [13]]. For the most recent study of these theories see also [14].Finally, the role of three-body interactions in the coilglobule [15] and polymer network [16] collapse transition is well known. It is of interest to study to what extent the data of Ref.[1] can be useful in this regard.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
