Specific retention volume, polymer

Figure 3.6 Variation of retention with the composition of the stationary phase in GLC. Stationary phase styrene-butadiene polymer blends and copolymers, the butadiene fraction is plotted on the horizontal axis, (a) Specific retention volumes for three n-alkanes and benzene. V is proportional to the capacity factor, (b) the retention index for benzene. The solid line is calculated from the straight lines in figure 3.6a. The circles (polymer blends) and triangles (copolymers) represent experimental data. Figure taken from ref. [310], Reprinted with permission.

Unfortunately, in many instances the materials employed as sensor coatings are nonvolatile solids (polymers) for which 6 values cannot be calculated directly. Solubility parameters for these materials can be estimated, however, by immersion testing [172b], inverse gas chromatography [173,174] or ftom coated-SAW sensor responses [166]. In inverse chromatography, the polymeric coating material is used as a stationary phase on a GC column, and the specific retention volumes (V ) for several solutes are determined. Since the Vg is directly related to, Kc, the solubility parameter for the polymer coating can be derived from relationships similar to Equation 5.32. A similar approach is used to derive S, from SAW sensor response data [166]. 

When studying polymer mixtures one needs to prepare packed columns containing an inert support coated with each of the base polymers and with the mixture, which therefore must be capable of being evaporated onto the support from a common solvent. Using a solvent probe one can then measure the specific retention volumes of the solvents when passed as vapour through the columns, i.e. V , V and V ... 

Perhaps a more important motivator for the increasing use of IGC is the method s flexibility and potential for generating data useful in the broad domain of polymer physical chemistry. Key to this consideration is the relationship between thermodynamics and the fundamental datum of IGC, the specific retention volume, Vg. The relationship has been... 

The specific retention volume, V°g defined as the net retention volume per unit weight of polymer, corrected to 273 K, is given by... 

IGC was used to determine the thermodynamic miscibility behavior of several polymer blends polystyrene-poly(n-butyl methacrylate), poly(vinylidene fluoride)-poly(methyl methacrylate), and polystyrene-poly(2,6-dimethyl-1,4-phenylene oxide) blends. Specific retention volumes were measured for a variety of probes in pure and mixed stationary phases of the molten polymers, and Flory-Huggins interaction parameters were calculated. A generally consistent and realistic measure of the polymer-polymer interaction can be obtained with this technique. 

The usefulness of inverse gas chromatography for determining polymer-small molecule interactions is well established (1,2). This method provides a fast and convenient way of obtaining thermodynamic data for concentrated polymer systems. However, this technique can also be used to measure polymer-polymer interaction parameters via a ternary solution approach Q). Measurements of specific retention volumes of two binary (volatile probe-polymer) and one ternary (volatile probe-polymer blend) system are sufficient to calculate xp3 > the Flory-Huggins interaction parameter, which is a measure of the thermodynamic... 

A procedure was developed in which the retention by the polymer was obtained by subtracting the retention of the support from the observed retention of a given column Vgol)S. According to this treatment, the specific retention volume is given by... 

Specific retention volumes and calculated 12 values for the three sets of polymer-probe pairs are given in Tables II to IV. In all cases, specific retention volumes were corrected for support retention. Retention diagrams for polystyrene and PMMPO are shown in Figures 2 to 3. 

A conceptual difficulty arises in characterizing polymer stationary phases with gas-liquid chromatographic probe-solute specific retention volumes (1), namely, since it is a matter of experience that V remains finite, the mole fraction-based solute activity coefficient x must asymptotically approach zero as the molecular weight of the polymer stationary phase Mg becomes large . ... 

These net retention volumes are reduced to specific retention volumes, by division of equation (2) with the mass of the liquid (here the Uquid is the molten polymer). They are corrected for the pressure difference between column inlet and outlet pressure, and reduced to a temperature To = 273.15 K. 

Preliminary experiments for MMA-SMA graftcopolymers were carried out to examine the surface activity of the graftcopolymers.5) Inverse gas chromatography, using a pol nner studied as the stationary phase, is a convenient and useful method for characterizing the surface and bulk properties of surface active copol nners. Polymers were coated on Chromosorb G (AW-DMCS treated, 60-80 mesh) from the chloroform solutions by evaporation. The polymer-coated supports were packed in a column and conditioned in the gas chromatograph oven at 160 for 5 hours. The specific retention volume for n-dodecane (where... 

Comparison of the specific retention volumes of hydrocarbons on poly-dimethylsiloxane [10], determined in two different laboratories by two groups of researchers over the temperature range 25—55°C differ by 3—5%. Similarly the determination of retention of n-decane and n-do-decane on linear polyethylene differs by 8% [11,12]. Braun et al. [12] determined the amount of polymer remaining after calcination and found that the support loses 0.2% of weight on drying and 0.46% on calcination. The application of corrections to the results obtained in reference [11] has improved the agreement however the discrepancy depends on the content of stationary phase for 5—6% stationary phase the difference is 7.5%, while for 10—11% it drops to 3.6%. The value determined for the content of stationary phase depends on the method, and so does the value of Vg Table 2.3 shows the difference between the concentra-... 

Equation (5.14) represents the link between the specific retention volumes 7 , calculated from chromatographic data, and the thermodynamic interaction parameter, as defined by the Flory-Huggins approach. This parameter depends on the polymer concentration, as has been proved experimentally [12, 13]. Orofino and Flory [14] have shown that the term Xi2 92 iu eqn (5.8) represents an incomplete expression for the non-configurational contribution to the activity, this must be written as a series of powers in terms of the volume fraction, the first term being Xi2[Pg.131]

For polar crystalline-amorphous polymers adsorption at the polymer-carrier gas interface becomes much more likely and the contribution of adsorption should be subtracted from the experimental specific retention volume both above and below In-... 

Fig. 5.6. — Illustration of the summing of specific retention volumes due to adsorption (curve 1) and dissolution (curve 2) to obtain the real retention diagram (curve 3) for a crystalline-amorphous polymer [171].

The specific retention volume is related to the properties of the polymer and solvent through the equation [10, 40] ... 

Gas-liquid Chromatography (g.l.c.).—Letcher has reviewed the use of g.l.c. to obtain activity coefficients in non-poiymer systems. The method is claimed - to be an accurate means of obtaining thermodynamic quantities in binary solutions when the two components differ considerably in volatility. Clearly this applies to many polymer-solvent systems and then the pol3rmer is conveniently made to form the stationary (liquid) phase in standard equipment. The solvent of interest is introduced into the mobile (gas) phase and its specific retention volume measured, from which heats of mixing are calculated > in the limit of zero concentration of solvent (a limit of interest in connection with the removal of volatiles from polymeric materials - ). 

The Flory-Huggins interaction parameter, which indicates the interaction of a vapor-phase probe at infinite dilution with a polymer, can be related to the specific retention volume of probes, Vg, by the following equation ... 

The procedure for IGC involves coating the stationary inert support material with the polymers and the blends and measuring the retention time according to GC protocols. The retention time is a function of the activity of the probe and can be used to qualitatively assess interactions in the polymer blend by employing probes such as hydrogen bonding, polar or non-polar probes. The key experimental parameter, V°, is the specific retention volume and is determined from ... 

A series of pure low molar mass solutes with different polarities, such as alkanes, acetates, alcohols, formic acid, dimethyl amine and water were injected into the chromatographic colunm that contains the polymer blend. Their interaction with the stationary phase will reveal the effect of the chemical nature of the injected solutes on their miscibility with the blend. Several chromatographic quantities, illustrated in Equation 1 are precisely measured directly from the IGC experiment. These quantities will yield the specific retention volume. Kg". Kg" is the key term in the calculation of thermodynamic parameters and is commonly used to describe the chromatographic elution behavior of solutes. It is defined as ... 

For some polymers, like polystyrene or poly(methyl methacrylate), narrow standards of known molar mass and small polydispersity are commercially available, which can be used for calibration. Unfortunately, such standards are not available for all polymers and then the obtained true molar masses of a specific polymer might differ by a factor of two from the value obtained by calibration with, e.g., polystyrene [30] (see Section 9.1). This problem can be resolved by the so-called universal calibration, which is based on the finding that the retention volume of a polymer is a single-valued function of the hydrodynamic volume of the polymer, irrespective of its chemical nature and... 

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