Semi-dilute solutions solvents

Viscoelastic properties have been discussed in relation to molar mass, concentration, solvent quality and shear rate. Considering the molecular models presented here, it is possible to describe the flow characteristics of dilute and semi-dilute solutions, as well as in simple shear flow, independent of the molar mass, concentration and thermodynamic quality of the solvent. The derivations can be extended to finite shear, i.e. it is possible to evaluate T) as a function of the shear rate. Furthermore it is now possible to approximate the critical conditions (critical shear rate, critical rate of elongation) at which the onset of mechanical degradation occurs. With these findings it is therefore possible to tune the flow features of a polymeric solution so that it exhibits the desired behaviour under the respective deposit conditions. 

For non-interacting, incompressible polymer systems the dynamic structure factors of Eq. (3) may be significantly simplified. The sums, which in Eq. (3) have to be carried out over all atoms or in the small Q limit over all monomers and solvent molecules in the sample, may be restricted to only one average chain yielding so-called form factors. With the exception of semi-dilute solutions in the following, we will always use this restriction. Thus, S(Q, t) and Sinc(Q, t) will be understood as dynamic structure factors of single chains. Under these circumstances the normalized, so-called macroscopic coherent cross section (scattering per unit volume) follows as... 

Based on the analogy between polymer solutions and magnetic systems [4,101], static scaling considerations were also applied to develop a phase diagram, where the reduced temperature x = (T — 0)/0 (0 0-temperature) and the monomer concentration c enter as variables [102,103]. This phase diagram covers 0- and good solvent conditions for dilute and semi-dilute solutions. The latter will be treated in detail below. 

A comparison with Burchard s first cumulant calculations shows qualitative agreement, in particular with respect to the position of the minimum. Quantitatively, however, important differences are obvious. Both the sharpness as well as the amplitude of the phenomenon are underestimated. These deviations may originate from an overestimation of the hydrodynamic interaction between segments. Since a star of high f internally compromises a semi-dilute solution, the back-flow field of solvent molecules will be partly screened [40,117]. Thus, the effects of hydrodynamic interaction, which in general eases the renormalization effects owing to S(Q) [152], are expected to be weaker than assumed in the cumulant calculations and thus the minimum should be more pronounced than calculated. Furthermore, since for Gaussian chains the relaxation rate decreases... 

It is generally accepted that in semi-dilute solutions under good solvent conditions both the excluded volume interactions and the hydrodynamic interactions are screened owing to the presence of other chains [4,5,103], With respect to the correlation lengths (c) and H(c) there is no consensus as to whether these quantities have to be equal [11] or in general would be different [160],... 

Under good solvent conditions the dynamics of semi-dilute solutions was investigated by NSE using a PDMS/d-benzene system at T = 343 K and various concentrations 0.02 c < 0.25. The critical concentration c as defined by (112) is 0.055. 

These models retain the form of the nonbonded interaction used in the chemically realistic modeling, i.e., they use either an interaction of the Lennard-Jones or of the exponential-6 type. The repulsive parts of these potentials generate the necessary local excluded volume, whereas the attractive long-range parts can be used to model varying solvent quality for dilute or semi-dilute solutions and to generate a reasonable equation-of-state behavior for polymeric melts. 

In semi dilute (c>c, [B] = 0.3-0.5 mole.l- ) or dilute (c< c, [B] = 10-2 mole.l- -) solution, Kp is significantly greater for copolymers than for the model compounds whatever the solvent is. For semi-dilute solution in a given solvent, the complex influences of composition, unit distribution and tacticity do not result in definite trends on K, values, as illustrated in table 6 by some representative Kj data related to keto-2-picolyl structures at 25°C. 

A semi-dilute solution has an entangled aspect similar to a network. An individual chain can be envisioned as constituted by a series of blobs of size equal to the transient network mesh size [16], which obviously decreases with increasing concentration. For c=c , is similar to the chain mean size. For c c, however, the mesh size is independent on the chain length. In a good solvent, according to Eqs. (5) and (6), these conditions are satisfied by ... 

Nj,=N/f is the number of beads per branch or arm). For larger chains, however, the solvent can penetrate in outer regions of the star and the situation within these regions is more Hke a concentrated solution or a semi-dilute solution. These portions of the arms constitute a series of blobs, whose sizes increase in the direction of the arm end. The surface of a sphere of radius r from the star center is occupied by f blobs. Then the blob size is proportional to rf. Most internal blobs are placed in conditions similar to concentrated solutions and, consequently, their squared size is proportional to the number of polymer units inside them as in an ideal chain. This permits one to obtain the density of units inside the blob, as a function of r ... 

Before discussing theoretical approaches let us review some experimental results on the influence of flow on the phase behavior of polymer solutions and blends. Pioneering work on shear-induced phase changes in polymer solutions was carried out by Silberberg and Kuhn [108] on a polymer mixture of polystyrene (PS) and ethyl cellulose dissolved in benzene a system which displays UCST behavior. They observed shear-dependent depressions of the critical point of as much as 13 K under steady-state shear at rates up to 270 s Similar results on shear-induced homogenization were reported on a 50/50 blend solution of PS and poly(butadiene) (PB) with dioctyl phthalate (DOP) as a solvent under steady-state Couette flow [109, 110], A semi-dilute solution of the mixture containing 3 wt% of total polymer was prepared. The quiescent... 

In semi-dilute solutions, the diffusion coefficient describing the thermal motion of the polymer chains that take part in an osmotic fluctuation in the surrounding solvent may be defined as follows... 

The solvent effects of 25 different solvents, including polar, dipolar, aprotic, and amphiprotic examples, on the tautomeric equilibrium of /-butyl quinaldyl ketone 121 (R1 = /-Bu R2 = H) in semi-dilute solutions have been studied by H NMR and UV spectroscopy. An increase in temperature or in solvent polarity shifts the 121a 121c equilibrium toward the ketimine tautomer 121a (82JHC785). 

Osmotic pressure of dilute and semi-dilute solutions in moderately good solvent one-loop approximation (b 0, c = 0)... 

In fact, it is always possible to compare the properties of polymers in moderately dilute or semi-dilute solutions with those which the same polymers would have in a very dilute solution. In other words, the size of an isolated JV-link polymer in a solvent can always be used as a scale length to describe the... 

Thus, the transition between poor and good solvent in a semi-dilute solution corresponds to a concentration C = C at which the screening effect begins to... 

The borderline between dilute and semi-dilute solutions intersects the borderline between poor and good solvents at a point the ordinate of which can be chosen as the value z0. Thus, by writing C = C and by comparing (13.2.154) with (13.2.156), we find... 

The universal constant f which in good solvent for a semi-dilute solution is given by... 

Chain concentration corresponding, for semi-dilute solutions, to the crossover between good and poor solvents... 

Fx Universal constant concerning the osmotic pressure of semi-dilute solutions in good solvent (for x > 1, F(x) a F, x 1 [Pg.916]

Number of swollen sequences constituting a polymer chain in a semi-dilute solution for a good solvent the size of a sequence is, by definition, the Kuhnian overlap length... 

Sophisticated experimental methods allow the development of models for polymers in dilute and semi-dilute solutions. Chain stiffness may be represented by the Kuhn segment lengths and determined in dilute solution. Models for cellulose and cellulose derivatives have recently been published whose main features are the irreversible aggregation of chains, if hydrogen bonding is possible even in dilute solutions. Trisubstituted cellulose derivatives or cellulose in hydrogen bond breaking solvents exist as molecular dispersed chains. How-... 

Figure 8. Schematic models for CTC in (a) dilute solution for small and large molecules, respectively, and (b) semi-dilute solution for small molecules. The dashed lines enclose domains with solvent shells (adapted from [11]).

To determine the critical solvent concentration, o, at which the diffusivity changes to a reptative mode, the following argument was applied. The characteristic crossover concentration for a change from a concentrated to a semi-dilute solution for polymer melts [63] is used as an initial estimate for uf ... 

In fact, as he illustrated, reported osmotic pressure data on many polymer + solvent systems can be fitted precisely with eq 1.10 over a range including both dilute and semi-dilute solutions. Thus, Schafer s equation should be quite useful for estimating 11 of polymer solutions over a relatively wide concentration range. 

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