Good solvent expansion

Q Range (A- ) (All Factors Included) No Good-Solvent Expansion No Hydro-dynamic Interaction No Variation ofC(4) [C(q) = const] No Internal Viscosity... 

In a good solvent, the end-to-end distance is greater than the 1q value owing to the coil expansion resulting from solvent imbibed into the domain of the polymer. The effect is quantitatively expressed in terms of an expansion factor a defined by the relationship... 

Although the emphasis in these last chapters is certainly on the polymeric solute, the experimental methods described herein also measure the interactions of these solutes with various solvents. Such interactions include the hydration of proteins at one extreme and the exclusion of poor solvents from random coils at the other. In between, good solvents are imbibed into the polymer domain to various degrees to expand coil dimensions. Such quantities as the Flory-Huggins interaction parameter, the 0 temperature, and the coil expansion factor are among the ways such interactions are quantified in the following chapters. 

What is especially significant about Eq. (9.68) is the observation that the coil expansion factor a definitely increases with M for good solvents, meaning that-all other things being equal longer polymer chains expand above their 0 dimensions more than shorter chains. Even though the dependence of a on... 

On macroscopic length scales, as probed for example by dynamic mechanical relaxation experiments, the crossover from 0- to good solvent conditions in dilute solutions is accompanied by a gradual variation from Zimm to Rouse behavior [1,126]. As has been pointed out earlier, this effect is completely due to the coil expansion, resulting from the presence of excluded volume interactions. 

The expansion of a polymer coil is determined by its interaction with the solvent. The more favorable the interaction between the polymer segments and the solvent molecules (good solvent), the better the polymer dissolves and the more the coil expands. 

The plateau adsorbances at constant molecular weight increased linearly with the square root of NaCl concentration. For the same NaCl concentration the adsorbance was nearly independent of the molecular weight. The thickness of the adsorbed layer was approximately proportional to the square root of the molecular weight for the Theta solvent (4.17 M NaCl). For good solvents of lower NaCl concentrations the exponent of the molecular weight dependence of the thickness was less than 0.5. At the same adsorbance and molecular weight the cube of the expansion factor at, defined by the ratio of the thicknesses for good solvent and for Theta solvent, was proportional to the inverse square root of NaCl concentration. 

Expansion of Thickness of the Adsorbed Layer. In the low salt concentration the large thickness compared with the case of the Theta solvent (4.17 M NaCl) is considered to be due to the electrostatic repulsion, i.e., the excluded volume effect of the adsorbed NaPSS chains. Usually, the expansion factor at, defined by the ratio of the thickness in good solvent and that in the Theta solvent, is used to quantitatively evaluate the excluded volume effect for the adsorbed polymers. 

This function also gives an accurate description of the behavior of a linear chain in a good solvent (the expansion of the chain size is scaled by the x variable) except for very high values of x, corresponding to short distances between units. These short distances are dominated by the correlation hole effect due to EV [16,26]. 

Equation 13 can be extended to non-6 conditions by multiplying by an expansion parameter Since it is known that the expansion paramenter is greater than unity for good solvents and less than unity for poor solvents. Equation 13 would predict that the slope of the D/Dq versus c line for c >c would decrease in good solvents and increase in poor solvents, in agreement with predictions from... 

Since the degree of expansion of the polymer coils is directly dependent on the solvating power of the solvent, under otherwise comparable conditions, both a and [q] provide a measure of the goodness of a solvent high values of a and [q] (at constant molecular weight and temperature) indicate remarkable coil expansion and therefore a good solvent. Low values of a and [q] indicate a bad solvent. For example, the values a for poly(vinyl acetate) in methanol and acetone are 0.60 and 0.72, respectively. 

There are a number of quantitative features of Eq. (14) which are important in relation to rapid diffusional transport in binary systems. The mutual diffusion coefficient is primarily dependent on four parameters, namely the frictional coefficient 21 the virial coefficients, molecular weight of component 2 and its concentration. Therefore, for polymers for which water is a good solvent (strongly positive values of the virial coefficients), the magnitude of (D22)v and its concentration dependence will be a compromise between the increasing magnitude of with concentration and the increasing value of the virial expansion with concentration. 

Calculations of the coefficient bt have also been made for homogeneous regular stars (2, 73) and regular combs (74). Random combs have been treated by Casassa and Tagami (75). Berry and Casassa (32) show that an approximate expression for the virial coefficient A2 in good solvents, in terms of the expansion factor a, which was derived for linear polymers ... 

For high molecular weight polymers in good solvents, fo] exceeds fo]0 because of coil expansion under nondraining conditions that is, as more solvent enters the coil domain than would be present under 0 conditions, Equation (92) continues to apply, with R replacing R2gfi. Using Equation (90) to quantify this expansion effect, we obtain... 

For dilute solutions in good solvents the net excluded volume is positive, and coil dimensions are expanded beyond their unperturbed values. The expansion... 

The foregoing discussion assumed that using a good solvent in place of a solvent has no significant effect on the ratio of viscosities. With some exception (32, 33), the evidence in the case of g shows the validity to be unimpaired for polydisperse as well as monodisperse systems (29, 34-36). It is expected that polymer expansion in good solvents would be in the same direction for branched and linear polymers in dilute and concentrated media so that any errors would be compensating. 

This means that the only effect of the q factor on the [77]-M relationship is that of the excluded volume due to coil expansion in a good solvent. It follows from Equations 8 and 16 that... 

Figure 4 shows a plot of the static expansion factor (o ) as a function of the relative temperature 0/T, where a is defined as Rg(T)/Rg(0) and r is the number of residues that may be one monomer unit or a number of repeat units. When T < 0 (water is a good solvent for PNIPAM), the data points are reasonably fitted by the line with r = 105 calculated on the basis of Flory-Huggins theory [15]. Similar results have also been observed for linear polystyrene in cyclohexane [25,49]. The theory works well in the good-solvent region wherein the interaction parameter (x) is expected to be... 

The intrinsic viscosities of the dendritic polymers are extremely small compared with those of linear polymer of the same MW [86,91]. Furthermore, the dendritic polymers expand very little in going from a 0 solvent to a good solvent [92]. This is to be expected. When steric congestion forces the polymer chains to expand in a 0 solvent, further expansion in a good solvent is limited. In this regard it is important to note that the 0 condition must be carefully specified. It is known that branched polymers have different 0 conditions to the linear counterpart [93]. 

The average extension of the chain in space can be modified by its interaction with the environment. This modification will occur in dilute solution, except in the special case where the chain is dissolved in a 0 solvent. The typical dilute solution is prepared using a good solvent, in which case the polymer-solvent interaction produces a positive excluded volume that causes expansion of a flexible chain. The introduction of the consequences of long-range interactions into the conformational description of a linear chain greatly complicates the theoretical description A5-181 The focus is on an expansion factor that can be defined as... 

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