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There have been several theories proposed to describe the separation mechanism of SEC
; however, a thermodynamic explanation , rather than a kinetic model  has proved most useful. As shown in Eq. (10), any partition or distribution process is a function of both an entropic term and an enthalpic term:
K = eAs,Re-AH,RT (10)
where ÄS and AH are the change in entropy and enthalpy, respectively, when solute is transferred from one phase to the other phase.
In SEC, however, enthalpic interactions are absent, and Eq. (10) becomes
Ê = eAS,K (11)
Here, AS is the change of conformational entropy of a polymer ; the driving force being the concentration gradient between the pore volume of the packing and interstitial volume of the column. If there is a large decrease in conformational entropy, as in a high molecular weight polymer diffusing into small pores, Ê approaches zero, and the polymer elutes at V0. For small molecules that can freely diffuse into and out of the pores of the packing, AS is zero, Ê approaches unity, and the solute elutes at V,. Thus, according to thermodynamic considerations, Ê is independent of flow rate and temperature, and depends only on the size and shape (hydrodynamic volume) of a polymer relative to the average size and shape of the pores of the packing. Separation in SEC is governed by molecular size, which takes into account molecular weight and molecular conformation or shape. As discussed in Section V.D, molecular size is usually expressed in terms of a molecular hydrodynamic volume.
Unlike other modes of separation, there is no temperature dependency in SEC, as shown in Eq. (11), and the elution volume of a peak will be independent of column temperature. Obviously, column efficiency or peak broadening will be affected by temperature, but the peak position of the first moment will remain constant. Furthermore, changes in polymer hydro-dynamic volume with temperature are generally small. Nevertheless, it is good practice to thermostat SEC columns to help maintain a constant flow rate and the baseline stability, especially when using a differential refractometer as the detector.
Size exclusion chromatography is a relative, not absolute, technique for determining molecular weight distribution. As such, the column must be calibrated with standards of known molecular weight to obtain a calibration curve, represented as a plot of logarithm of the molecular weight versus elution volume (see Fig. 2). The slope of the calibration curve is related to the con-formation of the polymer: an extended or rod-like chain will have a much steeper slope, than that of a more compact structure, such as a branched polymer. The extrapolated intercept of the calibration curve is related to the molecular density or molecular mass per unit hydro-dynamic volume of the polymer. Thus, a polystyrene calibration curve will be shifted upward when compared with that of polyethylene.
The calibration curve is used to convert detector output (response versus elution time) into a differential molecular weight distribution (Fig. 3). Because a molecular weight distri-
Figure 3 Transformation of the SEC detector output into a differential molecular weight distribution using a molecular weight calibration curve.
bution should represent a change in the amount or weight of a polymer relative to a change in molecular weight, dw/d\ogM is used as the ordinate, rather than the weight fraction w. To determine the weight fraction or a percentage of a sample at a given molecular weight, a cumulative distribution is used (Fig. 4), which represents the integrated form of the differential molecular weight distribution.
The four most commonly used calibration methods, described in the following, are (1) primarily calibration, (2) secondary calibration, (3) broad-molecular weight calibration, and (4) universal calibration (molecular-weight-sensitive detectors are discussed in Sec. XIII.C).
A. Primary Calibration
The most accurate approach to calibrate an SEC system is with monodisperse standards that are chemically and structurally similar to the samples being analyzed. The standards should cover the molecular weight separation range of the samples, should be well characterized in terms of molecular weight, and should be nearly monodisperse (d < 1.05). The number of standards used depends on the molecular weight range and the linearity of the calibration curve. Typically, between four and ten standards are required to define the calibration curve. All SEC software programs include curve-fitting routines for optimum calibration. The use of “mixed-bed” or “linear” columns give fairly linear calibration curves, and their application is highly recommended (see Sec. IX).